Subject: Re: 4 questions on different subjects Date: Mon, 26 Feb 2001 21:47:26 +0100 (CET) From: Yuli Rudyak If $W, \dim W=n$ is a compact contractble manifold then its boundary $V$ is a homology sphere. Indeed, by the Poincare duality we have H\sp i(W)= H \sb{n-i}(W,V)$. Furthermore, $H\sb k(W,V)=\tilde H\sb {k-1}(V)$ since $W$ is contractible. So, $H\sb k(V)=0$ for $k \ne n-1$, and $\tilde H\sb{n-1}(V)=H\sb n(W,V)=H\sp 0(W)=Z$. Yuli Rudyak > > ______________________________________________ > Subject: Homology of the boundary > Date: Mon, 26 Feb 2001 18:33:58 +0100 > From: David Cohen-Steiner > > What are the connections between the homology of a manifold and the > one of its boundary ? > Under which assumptions is the boundary of a contractible manifold > a homology sphere? What are the relevant tools? > Thanks, > > David > > >