Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Lusternik-Schnirelmann category and cobordism

Author: Harpreet Singh
Journal: Proc. Amer. Math. Soc. 102 (1988), 183-190
MSC: Primary 57R75,; Secondary 55M30
MathSciNet review: 915741
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Abstract: The Lusternik-Schnirelmann category of a manifold $ M$ is the smallest integer $ k$ that $ M$ can be covered by $ k$ open sets each of which is contractible in $ M$. It is an upper bound for the length of nonzero products of Stiefel-Whitney classes of $ M$. The object of this paper is to use this restriction, on the length of nonzero products, to investigate the cobordism classes of manifolds with category less than or equal to three.

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Article copyright: © Copyright 1988 American Mathematical Society