From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2397 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: preprint: Normed combinatorial homology and noncommutative tori Date: Fri, 18 Jul 2003 14:39:52 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" X-Trace: ger.gmane.org 1241018632 3951 80.91.229.2 (29 Apr 2009 15:23:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:23:52 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Jul 18 12:23:31 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jul 2003 12:23:31 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19dX1f-0006m8-00 for categories-list@mta.ca; Fri, 18 Jul 2003 12:20:03 -0300 X-OriginalArrivalTime: 18 Jul 2003 12:30:48.0156 (UTC) FILETIME=[6AC0D9C0:01C34D28] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 25 Original-Lines: 42 Xref: news.gmane.org gmane.science.mathematics.categories:2397 Archived-At: The following preprint is available in ps, at: http://www.dima.unige.it/~grandis/Bsy2.ps ___________ Normed combinatorial homology and noncommutative tori Marco Grandis Abstract. Cubical sets have a directed homology, studied in a previous paper and consisting of preordered abelian groups, with a positive cone generated by the structural cubes. By this additional information, cubical sets can provide a sort of "noncommutative topology", agreeing with some results of noncommutative geometry but lacking the metric aspects of C*-algebras. Here, we make such similarity stricter by introducing *normed* cubical sets and their *normed* directed homology, formed of normed preordered abelian groups. The normed cubical sets associated with "irrational rotations" have thus the same classification up to isomorphism as the well-known irrational rotation C*-algebras. MSC: 55U10, 81R60, 55Nxx. Keywords: Cubical sets, noncommutative C*-algebras, combinatorial homology, normed abelian groups. Marco Grandis Dipartimento di Matematica Universita` di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/