Cobordism classes of manifolds with category four

Singh, Harpreet

doi:10.1090/S0002-9947-1988-0973172-7

Cobordism classes of manifolds with category four
HTML articles powered by AMS MathViewer

by Harpreet Singh PDF

Trans. Amer. Math. Soc. 310 (1988), 619-628 Request permission

Abstract:

The Lusternik-Schnirelmann category of a manifold $M$ is the smallest integer $k$ such that $M$ can be covered by $k$ open sets each of which is contractible in $M$. The classification up to cobordism of manifolds with category $3$ was completed by the author in 1985. The object of this paper is to attempt a similar classification of manifolds with category $4$.

References

Peter G. Anderson, Cobordism classes of squares of orientable manifolds, Bull. Amer. Math. Soc. 70 (1964), 818–819. MR 169245, DOI 10.1090/S0002-9904-1964-11246-5
I. M. James, On category, in the sense of Lusternik-Schnirelmann, Topology 17 (1978), no. 4, 331–348. MR 516214, DOI 10.1016/0040-9383(78)90002-2
M. V. Mielke, Cobordism properties of manifolds of small category, Proc. Amer. Math. Soc. 21 (1969), 332–334. MR 236939, DOI 10.1090/S0002-9939-1969-0236939-2
J. Milnor, On the Stiefel-Whitney numbers of complex manifolds and of spin manifolds, Topology 3 (1965), 223–230. MR 180977, DOI 10.1016/0040-9383(65)90055-8
John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
Harpreet Singh, Lusternik-Schnirelmann category and cobordism, Proc. Amer. Math. Soc. 102 (1988), no. 1, 183–190. MR 915741, DOI 10.1090/S0002-9939-1988-0915741-1
N. E. Steenrod, Cohomology operations, Annals of Mathematics Studies, No. 50, Princeton University Press, Princeton, N.J., 1962. Lectures by N. E. Steenrod written and revised by D. B. A. Epstein. MR 0145525
Robert E. Stong, Notes on cobordism theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. Mathematical notes. MR 0248858
R. E. Stong, Cobordism and Stiefel-Whitney numbers, Topology 4 (1965), 241–256. MR 205262, DOI 10.1016/0040-9383(65)90009-1
René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 61823, DOI 10.1007/BF02566923
C. T. C. Wall, Determination of the cobordism ring, Ann. of Math. (2) 72 (1960), 292–311. MR 120654, DOI 10.2307/1970136