Date: Sat, 17 Jan 1998 19:21:53 -0500 (EST)
From: Claude Schochet <claude@math.wayne.edu>
Subject: For the topologist email list (fwd)

The following question is posted for Chris Phillips.  Another one
will be posted separately.  You may respond to the list or to Claude Schochet.

        I would like an example of a "nice" (see below) compact Hausdorff
space X and a torsion class c in H^3 (X; Z) such that there does _not_
exist any homotopy equivalence h : X ---> X with h^* (c) = -c. "Nice"
means preferably a compact manifold; next best would be a finite complex.
If the space is sufficiently nasty that the choice of cohomology is
relevant, it should be Cech. I have nice examples in which the only
failing is that c is not torsion, and somewhat nasty examples in which
the only failing is that I can only prove the nonexistence of
homeomorphisms h : X ---> X with h^* (c) = -c.
        To be useful, c must specifically be in the _third_ cohomology
group.


                                                ---Chris Phillips