Abstract: Given n-dimensional manifolds X and Y, a cobordism between them is an (n+1)-dimensional manifolds W whose boundary is the disjoint union of X and Y. With no extra constraints on W, existence problem has been resolved by the work of Pontryagin and Thom. However, the problem is more difficult if one puts extra constrains on the topology of W (e.g. its homology or homotopy groups). In this talk, I will discuss our recent work about pi-1 injective cobordisms, which is a generalization of boundary-incompressible 3-manifolds. We will also give some applications about finite group actions on 4-manifolds with isolated fixed points. This is a joint work with Zhongzi Wang (Peking University).
