Realizing homology classes up to cobordism

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.

4 pages, no figures

References in corpus (1)

• Global structure of the mod two symmetric algebra, H^*(BO;F_2), over the Steenrod Algebra