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 ----------------------------+----------------------------------------