Subject: 2 questions
Date: Wed, 30 Jan 2002 13:20:11 -0500 (EST)
From: Adam Sikora <sikora@CRM.UMontreal.CA>
To: Don Davis <dmd1@lehigh.edu>

Dear Don,

could you post the following two questions?

1. Can a nontrivial finite group act freely on a contractible, compact
space?
(Equivalently, can a finite group G have a compact classifying space BG?
Obviously, BG cannot be a finite CW-complex).

2. Assume that X is paracompact. Let BZ/p be a classifying space of Z/p.
Is X x BZ_p paracompact?
(The problem is that X x Y does not need to be paracompact even if
X,Y are paracompact.)

Thank you.

-- Adam S.