From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5715 Path: news.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Re: iterating the fundamental groupoid does not work, so..... Date: Thu, 29 Apr 2010 09:58:33 +0930 Message-ID: References: Reply-To: David Roberts NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1272626189 31829 80.91.229.12 (30 Apr 2010 11:16:29 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 30 Apr 2010 11:16:29 +0000 (UTC) To: Ronnie Brown Original-X-From: categories@mta.ca Fri Apr 30 13:16:28 2010 connect(): No such file or directory Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1O7oCo-0001eo-M0 for gsmc-categories@m.gmane.org; Fri, 30 Apr 2010 13:16:26 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1O7ndu-0004Yt-Fj for categories-list@mta.ca; Fri, 30 Apr 2010 07:40:22 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5715 Archived-At: On 29 April 2010 05:48, Ronnie Brown wrote: > I would like to make a further point about the topological fundamental > groupoid of X. The information on this shows that iterating the > fundamental groupoid does NOT lead to higher dimensional information on X. > > If this means what I think it means: applying Pi_1 to the arrows and objects of the topologised fundamental groupoid, then I agree. In a suitable bicategory of topological groupoids (where internal weak equivalences a la Bunge-Pare or Everaert-Kieboom***-*van der Linden are formally inverted) the topologised fundamental groupoid is equivalent to a groupoid sans topology - in fact it is equivalent to itself where the topology is replaced by the discrete topology. The topologised fundamental groupoid in this way encodes only the 1-type of the space. David Roberts [For admin and other information see: http://www.mta.ca/~cat-dist/ ]