Subject: 2 questions
Date: Wed, 30 Jan 2002 13:20:11 -0500 (EST)
From: Adam Sikora
To: Don Davis
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.