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
> _______________________________________________