Title: On the $H_1$-injective cobordisms between 3-manifolds 

Speaker: Zhongzi Wang, Peking University

Abstract: Call two closed oriented 3-manifolds $Y_0$ and $Y_1$ integrally (rationally) $H_1$-injective cobordant, if there is a cobordism $W$ from $Y_0$ to $Y_1$ such that the boundary inclusions $Y_i \to W$ induce an injection on integral (rational) first homology. We showed that under the connected-sum operation, the set of integrally (rationally) $H_1$-injective cobordism classes has a structure of abelian monoid.  We also characterized the rationally $H_1$-injective cobordism monoid. This is a joint work with Jianfeng Lin.