Osaka Journal of Mathematics

Realizing homology classes up to cobordism

Mark Grant, András SZŰCS, and Tamás Terpai

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It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod $2$ homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.

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Osaka J. Math., Volume 54, Number 4 (2017), 801-805.

First available in Project Euclid: 20 October 2017

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Primary: 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 57R95: Realizing cycles by submanifolds 57R42: Immersions 55P47: Infinite loop spaces 57R19: Algebraic topology on manifolds


Grant, Mark; SZŰCS, András; Terpai, Tamás. Realizing homology classes up to cobordism. Osaka J. Math. 54 (2017), no. 4, 801--805.

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