Vita of Donald M. Davis

Mathematical publications of Donald M. Davis

  1. Massey products and H(p,q)-systems, with Victor P. Snaith, Mathematische Zeitschrift, 132 (1973) 1-10.
  2. A vanishing theorem in homological algebra, with Donald W. Anderson, Commentarii Mathematici Helvetici, 48 (1973) 318-327.
  3. The antiautomorphism of the Steenrod algebra. Proc Amer Math Soc, 44 (1974) 235-236.
  4. Generalized homology and the generalized vector field problem, Quarterly Jour of Math, Oxford, 25 (1974) 169-193.
  5. Nonexistence of axial maps, Topology and its applications, Marcel Dekker Inc., New York, (1974) 137-141.
  6. The geometric dimension of some vector bundles over projective spaces, with Mark Mahowald, Transactions Amer Math Soc, 205 (1975) 295-316.
  7. A strong nonimmersion theorem for RP^{8k+7}, with Mark Mahowald, Bulletin of Amer Math Soc 81 (1975) 155-156.
  8. The immersion conjecture for RP^{8k+7}, Conference on Homotopy theory, Northwestern University, 1974. Symposia of Sociedad Matematica Mexicana, 1 (1975) 21-29.
  9. Editor, Conference on Homotopy Theory, Northwestern University, 1974, Symposia of Sociedad Matematica Mexicana, 1 (1975).
  10. Correction to Symmetries and operations in homotopy theory, with R. James Milgram, Notices of Amer Math Soc 22 (1975) p. A-30.
  11. The cohomology of the spectrum bJ, Boletin Sociedad Matematicas Mexicana, 20 (1975) 6-11.
  12. Immersions of complex projective spaces and the generalized vector field problem, with Mark Mahowald, Proc London Math Soc 35 (1977) 333-348.
  13. The homology of BO and some results about the Steenrod algebra, with E.H. Brown and F.P. Peterson, Proc Cambridge Philosophical Soc 81 (1977) 393-398.
  14. Immersions of projective spaces, with Mark Mahowald, Proc Symp in Pure Math 32 (1977) 155-158.
  15. The immersion conjecture for RP^{8k+7} is false, with Mark Mahowald, Transactions Amer Math Soc 236 (1978) 361-383.
  16. Connective coverings of BO and immersions of projective spaces, Pacific Jour Math 76 (1978) 33-41.
  17. The BP-coaction for projective spaces, Canadian Jour Math 30 (197 8) 45-53.
  18. Obstruction theory and ko-theory, with Mark Mahowald, Proc Evanston Homotopy Theory Conference, Lecture Notes in Math, Springer-Verlag, 658 (1978) 134-164.
  19. A nondesuspension theorem for stunted real projective spaces, with Mark Mahowald, Proc Amer Math Soc, 71 (1978) 143-146.
  20. Stable p-equivalences of stunted complex projective spaces, Indiana Univ Math Jour, 28 (1979) 23-34.
  21. BP-operations and maps of stunted complex projective spaces, Proc Waterloo Topology Conf, Lecture Notes in Math, Springer-Verlag, 741 (1979) 373-393.
  22. The orientability of vector bundles with respect to certain spectra, with S. Gitler, W. Iberkleid, and M. Mahowald, Boletin Sociedad Matematicas Mexicana, 24 (1979) 49-55.
  23. The Euler class for connective ko-theory and an application to immersions of quaternionic projective spaces, with Mark Mahowald, Indiana Univ Math Jour 28 (1979) 1025-1034.
  24. Nonimmersions of real projective spaces implied by BP, with Luis Astey, Boletin Sociedad Mathematicas Mexicana, 25 (1980) 15-22.
  25. Calculation of Lin's Ext groups, with W.H. Lin, M. Mahowald, and J.F. Adams, Math Proc Cambridge Philosophical Soc, 87 (1980) 459-469.
  26. v_1- and v_2-periodicity in stable homotopy theory, with Mark Mahowald, Amer Jour Math, 103 (1981) 615-659.
  27. The stable geometric dimension of vector bundles over real projective spaces, with S. Gitler and M. Mahowald, Transactions Amer Math Soc, 268 (1981) 39-62. Correction in same journal 280 (1983) 841-843.
  28. An infinite family in the cohomology of the Steenrod algebra, Jou r of Pure and Applied Algebra, 21 (1981) 145-150.
  29. On the Segal conjecture for Z_2\times Z_2, Proc Amer Math Soc, 83 (1981) 616-618.
  30. Some quotients of the Steenrod algebra, Proc Amer Math Soc, 83 (1981) 619-622.
  31. The nonrealizability of the quotient A//A_2 of the Steenrod algebra, with Mark Mahowald, Amer Jour Math, 104 (1982) 1211-1216.
  32. Ext over the subalgebra A_2 of the Steenrod algebra for stunted projective spaces, with Mark Mahowald, Current trends in algebraic topology , Conference Proc of Canadian Math Soc, 2 (1982) 297-343.
  33. On the cohomology of MO<8>, Adem Symp on Algebraic Topology, Contemporary Math, Amer Math Soc, 12 (1982) 91-104.
  34. The splitting of BO<8> \smash bo and MO<8> \smash bo, Transactions Amer Math Soc, 276 (1983) 671-684.
  35. Some new immersions and nonimmersions of real projective spaces, Proc Northwestern Homotopy Theory Conference, Contemporary Math, Amer Math Soc, 19 (1982) 51-64.
  36. Desuspensions of stunted projective spaces, Pacific Jour Math 113 (1984) 35-49.
  37. The spectrum (P\smash bo)_{-\infty}, with Mark Mahowald, Math Pro c Cambridge Philosophical Soc, 96 (1984) 85-94.
  38. Unstable BP-homology and desuspensions, with Martin Bendersky, Amer Jour Math 107 (1985) 833-852.
  39. Odd-primary bo-resolutions and K-theory localization, Illinois Ma th Jour 30 (1986) 79-100.
  40. A family of unstable Steenrod modules which includes those of G. Carlsson, Jour Pure and Applied Algebra, 35 (1985) 253-267. Correction in s ame journal, 45 (87) 97-98.
  41. A strong nonimmersion theorem for real projective spaces, Annals of Math 120 (1984) 517-528.
  42. Homotopy groups of some mapping telescopes, with Mark Mahowald, Algebraic Topology and Algebraic K-Theory, Annals of Math Studies 113, (1987), Princeton Univ Press, 126-151.
  43. Mapping telescopes and K_*-localizations, with Mark Mahowald and Haynes Miller, Algebraic Topology and Algebraic K-theory, Annals of Math Studies 113, (1987) Princeton Univ Press, 152-167.
  44. Immersions of real projective spaces, Proceedings of Lefschetz Conference, Contemporary Math, Amer Math Soc. 58 (1987) 31-42.
  45. The spectrum (P\smash BP<2>)_{-\infty}, with D. Johnson, J. Klippenstein, M. Mahowald, and S. Wegmann, Transactions of Amer Math Soc, 296 (1986) 95-110.
  46. Classification of the stable homotopy types of stunted real projective spaces, with Mark Mahowald, Pacific Jour Math, 125 (1986) 335-34 5.
  47. The bo-Adams spectral sequence: some calculations and a proof of its vanishing line, Seattle Homotopy Theory Volume, Springer-Verlag Lecture Notes 1286 (1987) 267-285.
  48. A new spectrum related to 7-connected cobordism, with Mark Mahowald, Proceedings of 1986 Conf. at Arcata, Cal., Lecture Notes in Math, Springer-Verlag 1370 (1989) 126-134.
  49. The use of a computer to suggest key steps in the proof of a theorem in topology, Proc Conf on Computers in Geometry and Topology, Univ of Illinois, Marcel Dekker (1988) 121-129.
  50. v_1-periodic Ext over the Steenrod algebra, with Mark Mahowald, Trans Amer Math Soc. 309 (1988) 503-516.
  51. On the complex bordism of classifying spaces, with Martin Bendersky, Proceedings of 1986 Conference at Arcata, Cal., Lecture Notes in Math, Springer-Verlag, 1370 (1989) 53-56.
  52. The complex bordism of groups with periodic cohomology, with Tony Bahri, Martin Bendersky, and Peter Gilkey, Trans. Amer. Math. Soc. (316) (1989) 673-688.
  53. The image of the stable J-homomorphism, with Mark Mahowald, Topology 28 (1989) 39-58.
  54. Integral Brown-Gitler spectra, with Fred Cohen, Paul Goerss, and Mark Mahowald, Proc. Amer. Math. Soc. 103 (1988) 1299-1304.
  55. The SO(n)-of-origin, with Mark Mahowald, Forum Math. 1 (1989) 239-250.
  56. v_1-periodicity in the unstable Adams spectral sequence, with Mark Mahowald, Math. Zeit 204 (1990) 319-339.
  57. v_1-periodic homotopy of Sp(2), Sp(3), and S^{2n}, with Mark Mahowald, Proceedings of 1988 Conference at Kinosaki, Springer-Verlag Lecture Notes in Math 1418 (1990) 219-237.
  58. Divisibility of generalized exponential and logarithmic coefficients, Proc Amer Math Soc 109 (1990) 553-558.
  59. Divisibility by 2 of Stirling-like numbers, Proc Amer Math Soc 110 (1990) 597-600.
  60. v_1-periodic homotopy groups of SU(n) at odd primes, Proc London Math Soc 43 (1991) 529-544.
  61. 2-primary v_1-periodic homotopy groups of SU(n), with Martin Bendersky, Amer Jour Math 114 (1991) 465-494.
  62. Three contributions to the homotopy theory of the exceptional Lie groups G_2 and F_4, with Mark Mahowald, Jour Math Soc Japan 43 (1991) 661-671.
  63. v_1-periodic homotopy groups of exceptional Lie groups--torsion-free cases, with Martin Bendersky and Mamoru Mimura, Trans Amer Math Soc 333 (1992) 115-136.
  64. The unstable Novikov spectral sequence for Sp(n), and the power series \sinh^{-1}(x), with Martin Bendersky, Proc. Adams Symposium, London Math Soc Lecture Notes Series 176 (1992) 73-86.
  65. Some remarks on v_1-periodic homotopy groups, with Mark Mahowald, Proc Adams Symposium, London Math Society Lecture Notes Series 176 (1992) 55-72.
  66. The Nature and Power of Mathematics, Princeton University Press, 1993. Reprinted by Dover in 2003.
  67. Immersions of projective spaces: a historical survey, Proc Int Conf in Algebraic Topology, Oaxtepec, Contemporary Math Series of Amer Math Soc. 146 (1993) 31-38.
  68. On the unstable Adams spectral sequence for SO and U, and splittings of unstable Ext groups, with A. K. Bousfield, Bol Soc Math Mex 37 (1992) 41-53.
  69. v_1-localizations of torsion spectra and spherically resolved spaces, with Mark Mahowald, Topology 32 (1993) 543-550.
  70. v_1-periodic homotopy groups of Sp(n), with Martin Bendersky and Mark Mahowald, Pac Jour Math 170 (1995) 319-378.
  71. 3-primary v_1-periodic homotopy groups of F_4 and E_6, with Martin Bendersky, Trans Amer Math Soc 344 (1994) 291-306.
  72. Computing v_1-periodic homotopy groups of spheres and certain Lie groups, Handbook of Algebraic Topology, El sevier (1995) 993-1049.
  73. Equivalences of some v_1-telescopes, Proc of Gitler Conference, Contemporary Math AMS 188 (1995) 81-92.
  74. Tractable formulas for v_1-periodic homotopy group s of SU(n) when n < p^2-p+2, with Huajian Yang, Forum Math 8 (1996) 585-620.
  75. Elements of large order in pi_*(SU(n)) , Topology 37 (1998) 293-327.
  76. Embeddings of real projective spaces, Boletin Sociedad Matematica Mexicana 4 (1998) 115-122.
  77. Some new embeddings and nonimmersions of real projective spaces, with Vitaly Zelov, Proceedings of Amer Math Soc 128 (2000) 3731-3740.
  78. 3-primary v1-periodic homotopy groups of E7, New York Journal of Mathematics 4 (1998) 185-221.
  79. Articles on Fractals, Neutral geometry, Non-Euclidean geometry, and Topology in Encyclopedia of Mathematics Education, RoutledgeFalmer, NY (2001).
  80. Learning and Teaching about Fractals, Fractals, Computer Graphics, and Mathematics Education, edited by M. Frame and B. Mandelbrot, Math Assn Amer (2002) 55-61.
  81. From Representation Theory to Homotopy Groups, Memoirs Amer Math Soc 759 (2002).
  82. The 1-line of the K-theory Bousfield-Kan spectral sequence for Spin(2n+1), with Martin Bendersky, Contemp Math AMS 279 (2001) 37-56.
  83. Compositions in the v1-periodic homotopy groups of spheres, with Martin Bendersky, Forum Math 15 (2003) 229-245.
  84. Nonimmersions of real projective spaces implied by tmf, with Robert Bruner and Mark Mahowald, Contemp Math Amer Math Soc 293 (2002) 45-68.
  85. A stable approach to an unstable homotopy spectral sequence with Martin Bendersky, Topology 42 (2003) 1261-1287.
  86. The K-completion of E6, Progress in Math, Birkhauser 215 (2003) 107-124.
  87. Editor, Recent Progress in Homotopy Theory, Contemporary Math Amer Math Soc 293 (2002).
  88. Generalized axial maps and Euclidean immersions of lens spaces, with Luis Astey and Jesus Gonzalez, Boletin Mexican Mathematical Society 9 (2003) 151-163.
  89. v1-periodic homotopy groups of SO(n), with Martin Bendersky, Memoirs of Amer Math Soc 815 (2004).
  90. Representation types and 2-primary homotopy groups of certain compact Lie groups, Homology, Homotopy, and Applications 5 (2003) 297-324.
  91. Stable geometric dimension of vector bundles over even-dimensional real projective spaces, with Martin Bendersky and Mark Mahowald, Trans Amer Math Soc 358 (2006) 1585-1603.
  92. The mathematical work of Sam Gitler, 1960-2003 Contemporary Math AMS, 407 (2006) 1-9.
  93. 2-primary v1-periodic homotopy groups of SU(n) revisited, with Katarzyna Potocka, Forum Math 19 (2007) 783-822.
  94. Stable geometric dimension of vector bundles over odd-dimensional real projective spaces, with Martin Bendersky, Bol Soc Mat Mex 12 (2006) 85-108.
  95. A number-theoretic approach to homotopy exponents of SU(n), with Zhi-Wei Sun, Jour Pure Appl Algebra 209 (2007) 57-69.
  96. Combinatorial congruences modulo prime powers, with Zhi-Wei Sun, Trans Amer Math Soc 359 (2007) 5525-5553.
  97. Odd-primary homotopy exponents of compact simple Lie groups, with Stephen Theriault, Geometry and Topology Monographs 13 (2008) 195-201.
  98. Some new immersion results for complex projective spaces, Proceedings of Edinburgh Mathematical Society 51 (2008) 27-44.
  99. ARML---Fire, Ice, and Lightning, PCTM Magazine 45 (2006) 14-16.
  100. Immersions of RP^{2^e-1}, with Giora Dula, Jesus Gonzalez, and Mark Mahowald, Algebraic and Geometric Topology 8 (2008) 997-1030.
  101. Nonimmersions of RP^n implied by tmf, revisited, with Mark Mahowald, Proceedings of Complex Cobordism Conference, HHA 10 (2008) 151-179.
  102. v1-periodic homotopy groups of the Dwyer-Wilkerson space, with Martin Bendersky, New York Journal of Mathematics, 14 (2008) 379-392 .
  103. Homotopy types and v1-periodic homotopy groups of p-compact groups, Topology and its Applications 156 (2008) 300-321.
  104. Divisibility by 2 and 3 of certain Stirling numbers, Integers 8 (2008) #A56, 25 pages.
  105. Editor of conference proceedings, Complex cobordism in homotopy theory: its impact and prospects, HHA 10 (2008).
  106. Projective product spaces, Jour of Topology 3 (2010) 265-279.
  107. Maximizing a combinatorial expression arising from crowd estimation, Int Jour Modern Math 5 (2010) 129-148.
  108. Markov analysis of APBA, a baseball simulation game, Jour Quant Analysis in Sports 7-3 (2011), 13 pages..
  109. Coefficients in powers of the log series, Integers 11 (2011) 177-184.
  110. Connective versions of TMF(3), with Mark Mahowald, International Journal of Modern Math 5 (2010) 223-252.
  111. The KO^*-rings of BT^m, the Davis-Januszkiewicz spaces and certain toric manifolds, with Astey, Bahri, Bendersky, Cohen, Gitler, Mahowald, Ray, and Wood, Jour Pure Appl Alg 218 (2014) 303-320.
  112. Vector fields on RP^m x RP^n, Proc Amer Math Soc 140 (2012) 4381-4388.
  113. Some new nonimmersion results for real projective spaces, Bol Soc Mat Mex 17 (2011) 159-166.
  114. Algebraic topology: there's an app for that, Math Horizons 19 (2011) 23-25.
  115. Divisibility by 2 of partial Stirling numbers, Functiones et Approximatio Commentarii Mathematici 49 (2013) 29-56.
  116. v1-periodic 2-exponents of SU(2^e) and SU(2^e + 1), Jour Pure Appl Alg 216 (2012) 1268-1272.
  117. For which p-adic integers x can Sum_k 1/binom(x,k)be defined?, Jour Combinatorics and Number Theory 4 (2012) 87-109.
  118. For which 2-adic integers x can Sum 1/binomial(x,k) be defined?, Jour Combinatorics and Number Theory 6 (2014) 65-68.
  119. Binomial coefficients involving infinite powers of primes, Amer Math Monthly 121 (2014) 734-737.
  120. p-adic Stirling numbers of the second kind, Fibonacci Quarterly 52 (2014) 226-235.
  121. Enumerating lattices of subsets, Advances and Applications in Discrete Math 13 (2014) 143-153.
  122. 2-adic partial Stirling functions and their zeros, Jour of Combinatorics 5 (2014) 355-378.
  123. Topological complexity of 2-torsion lens spaces and ku-(co)homology, Morfismos 18 (2014) 1-40.
  124. Real projective space as a space of planar polygons, Morfismos 19 (2015) 1-6.
  125. Topological complexity of some planar polygon spaces, Bol Soc Mat Mex, 23 (2017) 129--139.
  126. Topological complexity of spatial polygon spaces, Proc Amer Math Soc 144 (2016) 3643-3645.
  127. Topological complexity of planar polygon spaces with small genetic code, Forum Mathematicum., 29 (2017) 313--328.
  128. On the zero-divisor-cup-length of spaces of oriented isometry classes of planar polygons, Topology and its Applications 207 (2016) 43-53.
  129. On the cohomology classes of planar polygon spaces, Contemp Math AMS. 702 (2018) 85-89.
  130. Topological complexity (within 1) of the space of isometry classes of planar n-gons for sufficiently large n, JP Jour Geom Topology 20 (2017) 1-26.
  131. An approach to the topological complexity of the Klein bottle, Morfismos 21 (2017) 1-13.
  132. The symmetrized topological complexity of the circle, New York Jour Math 23 (2017) 593-602.
  133. An n-dimensional Klein bottle, Proc Royal Soc Edinburgh Section A Mathematics 149 (2019) 1207-1221.
  134. A lower bound for higher topological complexity for real projective space, Jour Pure Appl Algebra, 222 (2018) 2881-2887.
  135. Bounds for higher topological complexity of real projective space implied by BP, Boletin Sociedad Matematica Mexicana, 25 (2019) 701-712.
  136. BP-homology of elementary 2-groups:BP-module structure, Proc Amer Math Soc 147 (2019) 2255-2264.
  137. Manifold properties of planar polygon spaces, Topology and its Applications 250 (2018) 27-36.
  138. K-theory and immersions of spatial polygon spaces, Forum Math 31 (2019) 1369-1377.
  139. On the unordered configuration space C(RP^n,2), Boletin Sociedad Matematica Mexicana 26 (2020) 765-773.
  140. Geodesic complexity of n-dimensional Klein bottles, with David Recio-Mitter, New York Jour Math 27 (2021) 296-318.
  141. Geodesics in the configuration spaces of two points in R^n, Tblisi Math Jour 14 (2021) 149-162.
  142. Two robots moving geodesically on a tree, with Mike Harrison and David Recio-Mitter, Algebraic and Geometric Topology 22 (2022) 785-814
  143. Geodesic complexity for non-geodesic spaces, Boletin Sociedad Matematica Mexicana 28 (2022) 15 pp.
  144. Stiefel-Whitney classes and immersions of orientable and Spin manifolds, Steve Wilson, Topology and its Applications 307 (2022) 14 pp.
  145. The connected Morava K-theory of the second mod p Eilenberg-MacLane space, with Doug Ravenel and Steve Wilson, submitted.
  146. Gorenstein duality and universal coefficient theorems, with John Greenlees, Jour of Pure and Applied Algebra 227 (2023) 12 pp.
  147. The connective K-theory of the Eilenberg-MacLane space K(Z/p,2), with Steve Wilson, Glasgow Jour Math (2023) 33 pp.
  148. Isomorphism classes of cut loci for a cube, with Manyi Guo, Discrete Math 347 (2024) 10 pp.
  149. Geodesic complexity of a tetrahedron, to appear in Graduate Jour Math.
  150. Geodesic complexity of a cube, submitted.
  151. Geodesic complexity, survey paper prepared for volume "Geometry, topology, and AI."