Realizing homology classes up to cobordism

Mark Grant, András Szűcs, Tamás Terpai

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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

Bibliographical note

Acknowledgements.
Szucs and Terpai are supported by the National Research, Development and Innovation Office NKFIH (OTKA) Grant NK 112735 and partially supported by ERC Advanced Grant LDTBud.

Keywords

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

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