Subject: Re: two postings
Date: Wed, 30 Jan 2002 12:52:33 -1000 (HST)
From: Chris Allday
To: dmd1@lehigh.edu
Here are answers to Adam's questions.
1. If G is a non-trivial finite group acting on a contractible compact space,
then any prime order subgroup will have at least one fixed point. So the action
of G cannot be free.
2. If X is paracompact and if G is a compact Lie group, the X x BG is
paracompact. This can be seen by using Bourbaki, Topologie Generale, Ch.9,
sec.4, exercise 20(d).
Chris.
>
>Subject: 2 questions
>Date: Wed, 30 Jan 2002 13:20:11 -0500 (EST)
>From: Adam Sikora
>
>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.
>
----------------------------+----------------------------------------
Chris Allday | INTERNET: chris@math.hawaii.edu
Department of Mathematics |
University of Hawaii |
2565 The Mall | Phone: (808) 956-7217
Honolulu, Hawaii 96822 | Fax: (808) 956-9139
----------------------------+----------------------------------------