From: "David L. Johnson" <david.johnson@lehigh.edu>
Subject: Re: H^n(M,Z) for a noncompact n-manifold.
Date: Sat, 12 May 2001 16:13:28 -0400
Newsgroups: sci.math.research
Summary: Top cohomology class is zero

Scott Morrison wrote:
> 
> The n-th (co)homology group of a noncompact smooth n-manifold is trivial.
> (At least, I think!) Why exactly? :-)
> I'm actually only interested in the n=4 case, but I'm happy to hear about
> the general case.

One reason is that the manifold has a deformation retract to its
(n-1)-skeleton.
(Of course, the manifold has to be connected for this to be true).  

-- 

David L. Johnson

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