Subject: question for the list Date: Thu, 13 May 2004 08:56:51 -0400 (EDT) From: Jack Morava To: DON DAVIS Dear Don, Here's a proposed question for the list. I hope it's not silly: you may know the answer off the top of your head. Thanks, Jack (:+{)} &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& A (finite) group G acts on itself through conjugation, so its classifying space BG inherits a G-action. It's easy to see that the action of any element g on BG is homotopic to the identity. I've always assumed that the quotient map BG --> BG/G is a homotopy equivalence, but this doesn't follow from the remark above. [If C is a connected topological group acting on a space X then the action of any element of C is homotopic to the identity, but that doesn't imply that X --> X/C is an equivalence!] Is this in fact true, well-known, false...? Is there a standard (or accesible) reference for it either way?