From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4012 Path: news.gmane.org!not-for-mail From: Gaucher Philippe Newsgroups: gmane.science.mathematics.categories Subject: Preprint: Homotopical interpretation of globular complex by multipointed d-space Date: Sun, 14 Oct 2007 19:59:47 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019659 11302 80.91.229.2 (29 Apr 2009 15:40:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:40:59 +0000 (UTC) To: categories list Original-X-From: rrosebru@mta.ca Sun Oct 14 18:58:48 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 14 Oct 2007 18:58:48 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IhBJH-0005xE-Pi for categories-list@mta.ca; Sun, 14 Oct 2007 18:47:43 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 69 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:4012 Archived-At: Dear All, Here is a new preprint: Title: Homotopical interpretation of globular complex by multipointed d-space Abstract: Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CW-complex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such that the homotopy category is equivalent to the homotopy category of flows. The underlying category of this model category is a variant of M. Grandis' notion of d-space over a topological space colimit generated by simplices. This result enables us to understand the relationship between the framework of flows and other works in directed algebraic topology using d-spaces. It also enables us to prove that the underlying homotopy type functor of flows can be interpreted up to equivalences of categories as the total left derived functor of a left Quillen adjoint. Comment: 28 pages, 2 figures Url: http://www.pps.jussieu.fr/~gaucher/Mdtop.ps http://www.pps.jussieu.fr/~gaucher/Mdtop.pdf