||REALIZING HOMOLOGY CLASSES UP TO COBORDISM
Szűcs, András ,
Grant, markTerpai, Tamás
Osaka Journal of Mathematics
805 , 2017-10 , Osaka University and Osaka City University, Departments of Mathematics
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.