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 language | English |
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Pages (from-to) | 801-805 |
Number of pages | 5 |
Journal | Osaka Journal of Mathematics |
Volume | 54 |
Issue number | 4 |
Early online date | 20 Oct 2017 |
Publication status | Published - 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