Subject: Discussion List question
Date: Wed, 1 May 2002 13:05:31 -0400
From: Allen Hatcher <hatcher@polygon.math.cornell.edu>

In connection with the recent posts on homology of orientable double
covers of non-orientable manifolds, it is natural to ask:

What restrictions are there on the rational homology of closed
non-orientable manifolds?

A simple example is the product of a sphere and an even-dimensional real
projective space. More generally one can take connected sums of such
products, and of course connected sums with orientable manifolds. How
close does this come to realizing all possibilities for rational
homology?

Having written an algebraic topology text, I've developed quite a taste
for elementary questions like Stasheff's. Thanks for asking it, Jim, and
thanks to those who provided nice answers. I'll definitely put this in a
future edition of my book. Anyone know any more nice questions like this?

Allen Hatcher