Subject: Re: response and conf Date: Fri, 14 May 2004 13:59:09 -0700 From: Jim Lin To: Don Davis Don- I will be teaching the beginning graduate course in topology and wanted to ask the listserve if there are any recommendations for texts. I am currently leaning toward using Hatcher's book, but if someone has a better book, I would appreciate knowing about it. thanks, Jim At 02:46 PM 5/14/2004 -0400, you wrote: >Two postings: A response and a conf update..........DMD >______________________________________________________ > >Subject: Re: question & conf >Date: Fri, 14 May 2004 15:03:44 +0100 (BST) >From: Ian Leary > >For a discrete group G, the map BG ---> BG/G >is a homotopy equivalence if and only if G is >abelian, in which case G acts trivially on BG. > >The fundamental group of BG/G is the abelianization >of G. > >There is a way to think about this in terms of classifying >spaces for families of subgroups. Let G x G act on G by: > > (g,h).k = gkh^{-1}. > >This action is transitive and the stabilizer of the >identity element is the diagonal subgroup of elements >of the form (g,g) in G x G. > > Now take the usual construction of EG, as the simplicial >set with n-simplices the set G^{n+1}, with the given >action of G x G. A subgroup H of G x G fixes some point >of EG if and only if H is conjugate to a subgroup of the >diagonal copy of G. Furthermore, the fixed point set >for any such subgroup is contractible. It follows that >EG with this action of G x G is a classifying space for >a family F of subgroups of G x G. A group H is in >the family F if and only if H is conjugate to a subgroup >of the diagonal subgroup. > > Factoring out EG by the action of G x 1 gives BG, >and then factoring out by the rest of G x G gives BG/G. >This gives a way to see that the fundamental group of >BG/G is the abelianisation of G. I don't know what the >meaning of the higher homotopy groups of BG/G is. > > One could ask what homotopy types can occur as BG/G >for some discrete G, a sort of Kan-Thurston type question. > > Best wishes, > Ian Leary > >On Thu, 13 May 2004, Don Davis wrote: > > > Two postings: A question and a conference........DMD > > _____________________________________________________ > > > > Subject: question for the list > > Date: Thu, 13 May 2004 08:56:51 -0400 (EDT) > > From: Jack Morava > > > > Here's a proposed question for the list. > > > > 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? > ____________________________________________________ > >Subject: conference announcement >Date: Fri, 14 May 2004 11:48:25 -0400 >From: Rick Jardine > >Third Announcement: > > Algebraic Topological Methods in Computer Science, II > >Department of Mathematics >University of Western Ontario >London, Ontario, Canada > >July 16-20, 2004 > >The main areas to be covered by this conference include computational >geometry and topology, networks and concurrency theory. The meeting will >consist of twenty invited lectures, with additional sessions for shorter >lectures. > >The following mathematical scientists have agreed to speak: > >Saugata Basu (Georgia Tech) >Herbert Edelsbrunner (CS, Duke) >Robin Forman (Rice) >Eric Goubault (Commissariat a l'Energie Atomique, France) >Kathryn Hess (Lausanne) >Michael Joswig (Berlin) >Robert Kotiuga (Boston Univ.) >Dmitry Kozlov (KTH) >Reinhard Laubenbacher (Virginia Bioinformatics Institute) >Martin Raussen (Aalborg) >Vin de Silva (Stanford) >Afra Zomorodian (Stanford) > >All main lectures will be held in Room 110 of Middlesex College. > >There will be a session for contributed talks. Participants who would >like to speak in this session should send a title and abstract for their >lecture to one of the organizers. The contributed talks will be 20-30 >minutes in length, as time permits. > >Abstracts for both the main and contributed talks can be viewed at >http://at.yorku.ca/cgi-bin/amca/cano-01. > >Middlesex College is the unique building on the campus of the University >of Western Ontario having a clock tower, and houses the departments of >Mathematics, Applied Mathematics and Computer Science. > >Housing: A block of rooms has been reserved for conference participants >at the Station Park Hotel (242 Pall Mall Street, London, Ontario, >Canada). Participants will be making their own reservations, by calling >800-561-4574 or 519-642-4444 or by sending e-mail to >hotel@stationparkinn.ca. The rate for participants is $105.00 CDN per >night - and the group booking name is the conference title: "Algebraic >Topological Methods". > >For alternative housing arrangements, see Dan Christensen's housing web >page http://jdc.math.uwo.ca/hotels.php. This page also contains links >to travel directions and restaurant listings. > >The University of Western Ontario runs a bed and breakfast operation in >Essex Hall (a residence on campus) during the summer months. The cost is >between $29.00 and $43.00 CDN per night, and there is high speed >internet access in the rooms. You can find further information and make >reservations online at http://www.uwo.ca/hfs/cs/. > >This conference has been funded by grants from the National Science >Foundation and the Fields Institute. Limited financial support may be >available for conference participants, especially for grad students and >postdocs. > >The most up to date information concerning the conference is available >at the web page http://www.math.uwo.ca/~jardine/at-csII.html. > >The organizers for this meeting are: > >Gunnar Carlsson: gunnar@math.stanford.edu >Rick Jardine: jardine@uwo.ca > >We ask that you advise one of us if you intend to come to the meeting.