Subject: Re: 3 postings
Date: Mon, 29 Apr 2002 12:49:30 -0400 (EDT)
From: Walter Neumann <neumann@math.columbia.edu>
To: Don Davis <dmd1@lehigh.edu>

>
> Subject: `wellknown'?
> Date: Sun, 28 Apr 2002 17:18:52 -0400
> From: jim stasheff <stasheff@email.unc.edu>
>
> 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

There is a 2-fold cover of the Klein bottle by the Klein bottle which
would seem to contradict this for k=1, n=2 ?

-walter neumann