Realizing homology classes up to cobordism

Mark Grant, András Szűcs, Tamás Terpai

Research output: Contribution to journalArticle

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Abstract

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.
Original languageEnglish
Pages (from-to)801-805
Number of pages5
JournalOsaka Journal of Mathematics
Volume54
Issue number4
Early online date20 Oct 2017
Publication statusPublished - Oct 2017

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Cobordism
Immersion
Homology
Finite Set
Sufficient
Class

Keywords

  • math.AT
  • immersions
  • cobordism
  • infinite loop space
  • realizing homology classes
  • singular maps

Cite this

Grant, M., Szűcs, A., & Terpai, T. (2017). Realizing homology classes up to cobordism. Osaka Journal of Mathematics, 54(4), 801-805.

Realizing homology classes up to cobordism. / Grant, Mark; Szűcs, András; Terpai, Tamás.

In: Osaka Journal of Mathematics, Vol. 54, No. 4, 10.2017, p. 801-805.

Research output: Contribution to journalArticle

Grant, M, Szűcs, A & Terpai, T 2017, 'Realizing homology classes up to cobordism', Osaka Journal of Mathematics, vol. 54, no. 4, pp. 801-805.
Grant, Mark ; Szűcs, András ; Terpai, Tamás. / Realizing homology classes up to cobordism. In: Osaka Journal of Mathematics. 2017 ; Vol. 54, No. 4. pp. 801-805.
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