Realizing homology classes up to cobordism

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

Bibliographical note

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.


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


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