Subject: query
From: "Dr A. J. Baker"
Date: Thu, 16 Nov 2006 16:59:46 -0000 (GMT)
Dear Jim,
Have a look at Prop 2.1 of
MR0232393 (38 #718)
Segal, Graeme
Classifying spaces and spectral sequences.
Inst. Hautes Études Sci. Publ. Math. No. 34 1968 105--112.
available through
http://www.numdam.org/
The point is to take F_0=id and F_1=g( )g^{-1} in the group as
a one object category.
Best wishes,
Andy
Dr A. J. Baker
Department of Mathematics
University of Glasgow
Glasgow
G12 8QW
Scotland
phone (0141) 330 6140
fax (0141) 330 4111
a.baker@maths.gla.ac.uk
http://www.maths.gla.ac.uk/~ajb/
_____________________________________________________________
From: Jack Morava
Date: Thu, 16 Nov 2006 12:15:27 -0500 (EST)
Dear Don,
I'm not sure this is relevant to Jim's question, but
I got confused by related issues in
HKR characters and higher twisted sectors, math.AT/0208235
now published in
Gromov-Witten theory of spin curves and orbifolds.
Proceedings of the AMS Special Session held at San Francisco State
University, San Francisco, CA, May 3--4, 2003. Edited by Tyler J. Jarvis,
Takashi Kimura and Arkady Vaintrob. Contemporary Mathematics, 403,
cf. \S 2.3, where Ian Leary kindly saved my bacon:
The action of G on BG is by homotopic maps, but they are not in
general homotopic as base-pointed maps. Leary showed that
\pi_1(BG/G) \cong H_1(G,\Z)
is the abelianization of G.
I'm cc'ing this to IL for a reality check, because I mite still have
things wrong...