Subject: Re: `wellknwon'? Date: Mon, 29 Apr 2002 10:33:17 -0400 From: John Klein Organization: Wayne State University To: Don Davis This is news to me. Maybe I am misunderstanding the question(?): Let S^3 --> P^3 be the universal cover. Then n = 3. Now choose k = 3. Then b_3(S^3) = 1. But b_3(P^3) + b_0(P^3) = 2. > > Subject: `wellknown'? > Date: Sun, 28 Apr 2002 17:18:52 -0400 > From: jim stasheff > > The following was news to me and does not seem to be in the obvious > texts: > > Let X --> Y be a 2-fold covering space where X and Y are n-manifolds. > Let b_k dentoe the k-th betti number. > > Claim: b_k (X) = b_k (Y) + b_{n-k} (Y) > > anyone know a reference? > > jim > _______________________________________________