Mathematics research publications of Donald M. Davis
Papers near the end of the list can be viewed by clicking on them.
- Massey products and H(p,q)-systems, with Victor P. Snaith,
Mathematische Zeitschrift, 132 (1973) 1-10.
- A vanishing theorem in homological algebra, with Donald W.
Anderson, Commentarii Mathematici Helvetici, 48 (1973) 318-327.
- The antiautomorphism of the Steenrod algebra.
Proc Amer Math Soc, 44 (1974) 235-236.
- Generalized homology and the generalized vector field problem,
Quarterly Jour of Math, Oxford, 25 (1974) 169-193.
- Nonexistence of axial maps, Topology and its applications, Marcel
Dekker Inc., New York, (1974) 137-141.
- The geometric dimension of some vector bundles over projective
spaces, with Mark Mahowald, Transactions Amer Math Soc, 205 (1975) 295-316.
- A strong nonimmersion theorem for RP^{8k+7}, with Mark Mahowald,
Bulletin of Amer Math Soc 81 (1975) 155-156.
- The immersion conjecture for RP^{8k+7}, Conference on Homotopy
theory, Northwestern University, 1974. Symposia of Sociedad Matematica
Mexicana, 1 (1975) 21-29.
- Editor, Conference on Homotopy Theory, Northwestern University,
1974, Symposia of Sociedad Matematica Mexicana, 1 (1975).
- Correction to Symmetries and operations in homotopy theory, with
R. James Milgram, Notices of Amer Math Soc 22 (1975) p. A-30.
- The cohomology of the spectrum bJ, Boletin Sociedad Matematicas
Mexicana, 20 (1975) 6-11.
- Immersions of complex projective spaces and the generalized vector
field problem, with Mark Mahowald, Proc London Math Soc 35 (1977) 333-348.
- 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.
- Immersions of projective spaces, with Mark Mahowald, Proc Symp in
Pure Math 32 (1977) 155-158.
- The immersion conjecture for RP^{8k+7} is false, with Mark
Mahowald,
Transactions Amer Math Soc 236 (1978) 361-383.
- Connective coverings of BO and immersions of projective spaces,
Pacific Jour Math 76 (1978) 33-41.
- The BP-coaction for projective spaces, Canadian Jour Math 30 (197
8)
45-53.
- Obstruction theory and ko-theory, with Mark Mahowald, Proc
Evanston Homotopy Theory Conference, Lecture Notes in Math, Springer-Verlag,
658 (1978) 134-164.
- A nondesuspension theorem for stunted real projective spaces,
with Mark Mahowald, Proc Amer Math Soc, 71 (1978) 143-146.
- Stable p-equivalences of stunted complex projective spaces,
Indiana Univ Math Jour, 28 (1979) 23-34.
- BP-operations and maps of stunted complex projective spaces, Proc
Waterloo Topology Conf, Lecture Notes in Math, Springer-Verlag, 741 (1979)
373-393.
- 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.
- 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.
- Nonimmersions of real projective spaces implied by BP, with Luis
Astey, Boletin Sociedad Mathematicas Mexicana, 25 (1980) 15-22.
- 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.
- v_1- and v_2-periodicity in stable homotopy theory, with
Mark Mahowald, Amer Jour Math, 103 (1981) 615-659.
- 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.
- An infinite family in the cohomology of the Steenrod algebra, Jou
r
of Pure and Applied Algebra, 21 (1981) 145-150.
- On the Segal conjecture for Z_2\times Z_2, Proc Amer Math Soc, 83
(1981) 616-618.
- Some quotients of the Steenrod algebra, Proc Amer Math Soc, 83
(1981) 619-622.
- The nonrealizability of the quotient A//A_2 of the
Steenrod algebra, with Mark Mahowald, Amer Jour Math, 104 (1982) 1211-1216.
- 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.
- On the cohomology of MO<8>, Adem Symp on Algebraic
Topology, Contemporary Math, Amer Math Soc, 12 (1982) 91-104.
- The splitting of BO<8> \smash bo and MO<8> \smash bo,
Transactions Amer Math Soc, 276 (1983) 671-684.
- Some new immersions and nonimmersions of real projective spaces,
Proc
Northwestern Homotopy Theory Conference, Contemporary Math, Amer Math Soc, 19
(1982) 51-64.
- Desuspensions of stunted projective spaces, Pacific Jour Math 113
(1984) 35-49.
- The spectrum (P\smash bo)_{-\infty}, with Mark Mahowald, Math Pro
c
Cambridge Philosophical Soc, 96 (1984) 85-94.
- Unstable BP-homology and desuspensions, with Martin Bendersky,
Amer Jour Math 107 (1985) 833-852.
- Odd-primary bo-resolutions and K-theory localization, Illinois Ma
th
Jour 30 (1986) 79-100.
- 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.
- A strong nonimmersion theorem for real projective spaces, Annals
of Math 120 (1984) 517-528.
- 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.
- 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.
- Immersions of real projective spaces, Proceedings of Lefschetz
Conference, Contemporary Math, Amer Math Soc. 58 (1987) 31-42.
- 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.
- Classification of the stable homotopy types of stunted real
projective spaces, with Mark Mahowald, Pacific Jour Math, 125 (1986) 335-34
5.
- 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.
- 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.
- 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.
- v_1-periodic Ext over the Steenrod algebra, with Mark Mahowald,
Trans Amer Math Soc. 309 (1988) 503-516.
- 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.
- The complex bordism of groups with periodic cohomology, with Tony
Bahri, Martin Bendersky, and Peter Gilkey, Trans. Amer. Math. Soc. (316)
(1989) 673-688.
- The image of the stable J-homomorphism, with Mark Mahowald,
Topology 28 (1989) 39-58.
- Integral Brown-Gitler spectra, with Fred Cohen, Paul Goerss, and
Mark Mahowald, Proc. Amer. Math. Soc. 103 (1988) 1299-1304.
- The SO(n)-of-origin, with Mark Mahowald,
Forum Math. 1 (1989) 239-250.
- v_1-periodicity in the unstable Adams spectral sequence, with
Mark Mahowald, Math. Zeit 204 (1990) 319-339.
- 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.
- Divisibility of generalized exponential and logarithmic
coefficients, Proc Amer Math Soc 109 (1990) 553-558.
- Divisibility by 2 of Stirling-like numbers, Proc
Amer Math Soc 110 (1990) 597-600.
- v_1-periodic homotopy groups of SU(n) at odd primes,
Proc London Math Soc 43 (1991) 529-544.
- 2-primary v_1-periodic homotopy groups of SU(n), with Martin
Bendersky, Amer Jour Math 114 (1991) 465-494.
- 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.
- 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.
- 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.
- Some remarks on v_1-periodic homotopy groups, with Mark Mahowald,
Proc Adams Symposium, London Math Society Lecture Notes Series 176 (1992)
55-72.
- 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.
- 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.
- v_1-localizations of torsion spectra and spherically resolved
spaces, with Mark Mahowald, Topology 32 (1993) 543-550.
- v_1-periodic homotopy groups of Sp(n), with
Martin Bendersky and Mark Mahowald, Pac Jour Math 170 (1995) 319-378.
- 3-primary v_1-periodic homotopy groups of F_4 and E_6, with
Martin Bendersky, Trans Amer Math Soc 344 (1994) 291-306.
- Computing v_1-periodic homotopy groups of spheres
and certain Lie groups, Handbook of Algebraic Topology, El
sevier (1995) 993-1049.
- Equivalences of some v_1-telescopes,
Proc of Gitler
Conference, Contemporary Math AMS 188 (1995) 81-92.
- 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.
- Elements of large order in pi_*(SU(n))
, Topology 37 (1998) 293-327.
- Embeddings of real projective spaces,
Boletin Sociedad Matematica Mexicana 4 (1998) 115-122.
- Some new embeddings and nonimmersions of real
projective spaces, with Vitaly Zelov,
Proceedings of Amer Math Soc 128 (2000) 3731-3740.
-
3-primary v1-periodic homotopy groups of E7,
New York Journal of Mathematics 4 (1998) 185-221.
- From Representation Theory to Homotopy
Groups, Memoirs Amer Math Soc 759 (2002).
-
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.
-
Compositions in the v1-periodic homotopy groups of spheres,
with Martin Bendersky, Forum Math 15 (2003) 229-245.
- Nonimmersions of real projective spaces implied
by tmf, with Robert Bruner and Mark Mahowald,
Contemp Math Amer Math Soc 293 (2002) 45-68.
- A stable approach to an unstable homotopy
spectral sequence with Martin Bendersky, Topology 42 (2003)
1261-1287.
- The K-completion of E6, Progress in
Math, Birkhauser 215 (2003) 107-124.
- Editor, Recent Progress in Homotopy Theory, Contemporary Math
Amer Math Soc 293 (2002).
- Generalized axial maps and Euclidean
immersions of lens spaces, with Luis Astey and Jesus Gonzalez,
Boletin Mexican Mathematical Society 9 (2003) 151-163.
- v1-periodic homotopy groups of
SO(n), with Martin Bendersky, Memoirs of Amer Math
Soc 815 (2004).
- Representation types and 2-primary
homotopy groups of certain compact Lie groups, Homology,
Homotopy, and Applications 5 (2003) 297-324.
- 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.
- The mathematical work of Sam Gitler,
1960-2003 Contemporary Math AMS, 407 (2006) 1-9.
- 2-primary v1-periodic homotopy groups of
SU(n) revisited, with Katarzyna Potocka, Forum Math 19 (2007)
783-822.
- Stable geometric dimension of vector
bundles over odd-dimensional real projective spaces, with Martin
Bendersky, Bol Soc Mat Mex 12 (2006) 85-108.
- A
number-theoretic approach to homotopy exponents of SU(n), with
Zhi-Wei Sun, Jour Pure Appl Algebra 209 (2007) 57-69.
- Combinatorial congruences modulo prime
powers, with Zhi-Wei Sun, Trans Amer Math Soc 359 (2007)
5525-5553.
- Odd-primary homotopy exponents of compact
simple Lie groups, with Stephen Theriault, Geometry
and Topology Monographs 13 (2008) 195-201.
- Some new immersion results for complex
projective spaces, Proceedings of Edinburgh
Mathematical Society 51 (2008) 27-44.
- Immersions of RP^{2^e-1}, with
Giora Dula, Jesus Gonzalez, and Mark Mahowald, Algebraic and
Geometric
Topology 8 (2008) 997-1030.
- Nonimmersions
of RP^n implied by tmf,
revisited, with Mark Mahowald, Proceedings of
Complex Cobordism Conference, HHA, 10 (2008) 151-179.
- v1-periodic homotopy groups of the
Dwyer-Wilkerson space, with Martin Bendersky, New
York Journal of Mathematics, 14 (2008) 379-392 .
- Homotopy types and v1-periodic homotopy
groups
of p-compact groups, Topology and its
Applications 156 (2008) 300-321.
- Divisibility by 2 and 3 of certain Stirling
numbers, Integers 8 (2008) #A56, 25 pages.
- Editor of conference proceedings,
Complex cobordism in homotopy theory: its impact and prospects, HHA 10
(2008).
- Projective product spaces,
Journal of Topology 3 (2010) 265-279.
- Maximizing a combinatorial expression
arising from crowd estimation, International Journal of Modern
Math 5 (2010) 129-148.
- Coefficients in powers of the log
series, Integers 11 (2011) 177-184.
- Connective versions of TMF(3),
with Mark Mahowald, International Journal of Modern Math 5 (2010) 223-252.
- 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.
- Vector fields on RP^m x RP^n,
Proc Amer Math Soc 140 (2012) 4381-4388.
- Some new nonimmersion results for real
projective spaces, Bol Soc Mat Mex 17 (2011) 159-166.
- Algebraic topology: there's an app for
that, Math Horizons 19 (2011) 23-25.
- Divisibility by 2 of partial Stirling
numbers, Functiones et Approximatio Commentarii
Mathematici 49 (2013) 29-56.
- v1-periodic 2-exponents of SU(2^e) and SU(2^e
+ 1), Jour Pure Appl Alg 216 (2012) 1268-1272.
- For which p-adic integers x can Sum
1/binomial(x,k) be defined?, Jour Combinatorics and
Number Theory 4 (2012) 87-104.
- For which 2-adic integers x can Sum
1/binomial(x,k) be defined?, Jour Combinatorics and Number Theory 6 (2014) 215--218.
- Binomial coefficients involving infinite powers
of primes, Amer Math Monthly 121 (2014) 734-737.
- p-adic Stirling numbers of the second
kind, Fibonacci Quarterly 52 (2014) 226-235.
- Enumerating lattices of subsets
, Advances and Applications in Discrete Math 13 (2014) 143-153.
- 2-adic partial Stirling functions and their zeros, Jour of Combinatorics 5 (2014) 355-378.
- Topological complexity of 2-torsion lens spaces and ku-(co)homology, Morfismos 18 (2014) 1-40.
- Real projective space as a space of planar polygons, Morfismos 19 (2015) 1-6.
- Topological
complexity of some planar polygon spaces, Bol Soc Mat 23 (2017) 129-139.
- Topological complexity of spatial
polygon spaces, Proc Amer Math Soc 144 (2016) 3643-3645.
- Topological complexity of planar polygon
spaces with small genetic code, Forum
Mathematicum 29 (2017) 313--328.
- On the zero-divisor-cup-length of spaces
of oriented isometry classes of planar polygons,
Topology and its Applications 207 (2016) 43-53.
- On the cohomology classes of planar
polygon spaces, Contemp Math AMS 702 (2018) 85--89.
- Topological complexity (within 1) of the space
of isometry classes of planar n-gons for sufficiently large n, JP Journal of Geometry and Topology 20 (2017) 1-26.
- An approach to the topological complexity of the Klein
bottle, Morfismos 21 (2017) 1-13.
- The symmetrized topological complexity of the circle, New York Jour Math 23 (2017) 593--602.
- An n-dimensional Klein bottle, Proc Royal Society Edinburgh, Section A, Mathematics 149 (2019) 1207--1221..
- Explicit motion planning rules in certain polygon spaces, addendum to preceding paper, probably not for publication.
- A lower bound for higher topological complexity for real projective space, Journal of Pure and Applied Algebra 222 (2018) 2881--2887.
- BP-homology of elementary abelian 2-groups: BP-module structure, Proc Amer Math Soc 147 (2019) 2255-2264.
- Bounds for higher topological complexity of real projective space implied by BP, Boletin Sociedad Matematica Mexicana 25 (2019) 701--712.
- Manifold properties of planar polygon spaces, Topology and its Applications 250 (2018) 27-36.
- K-theory and immersions of spatial polygon spaces, Forum Mathematicum 31 (2019) 1369--1377.
- On the unordered configuration space C(RP^n,2), Boletin Sociedad Matematica Mexicana 26 (2020) 765-773.
- The geodesic complexity of n-dimensional Klein bottles, with David Recio-Mitter, New York Jour Math 27 (2021) 296-318.
- Geodesics in the configuration spaces of two points in R^n, Tblisi Math Jour 14 (2021) 149--162..
- Two robots moving geodesically on a tree, with Mike Harrison and David Recio-Mitter, Algebraic and Geometric Topology, 22 (2022) 785-814.
- Geodesic complexity for non-geodesic spaces, Boletin Sociedad Matematics Mexicana, 28 (2022) paper #8, 18 pp.
- Stiefel-Whitney classes and immersions of orientable and Spin manifolds, with Steve Wilson, Topology and its Applications, 307 (2022) paper #107780, 14 pp.
- The connected Morava K-theory of the Eilenberg-MacLane space K(Z/p,2), with Doug Ravenel and Steve Wilson, submitted.
- Duality in BP (co)homology, on arXiv, subsumed into paper with Greenlees.
- The connective K-theory of the Eilenberg-MacLane space K(Z/p,2), with Steve Wilson, Glasgow Math Jour 66 (2024) 188-220.
- Gorenstein duality and universal coefficient theorems, with John Greenlees, Jour Pure Appl Alg, 227 (2023) paper #107265, 12 pp.
- Isomorphism classes of cut loci for a cube, with Manyi Guo, Discrete Math 347 (2024) .
- Geodesic complexity of a tetrahedrom, Graduate Jour Math. 8 (2023) 15-22.
- Geodesic complexity of a cube, Bol Mat Soc Mex.20 (2024) paper #38, 16pp.
- Geodesic complexity, Topology and AI," European Math Society Series in Industrial and Applied Mathematics (2024) 291--307.
- The cohomology of the connective spectra for K-theory revisited, with Steve Wilson, New York Jour Math 30 (2024) 513-520.
- The connective KO-theory of the Eilenberg-MacLane space K(Z_2,2), I: the E_2 page, with Steve Wilson, submitted.