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.
|Number of pages||5|
|Journal||Osaka Journal of Mathematics|
|Early online date||20 Oct 2017|
|Publication status||Published - Oct 2017|
- inﬁnite loop space
- realizing homology classes
- singular maps