From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3810 Path: news.gmane.org!not-for-mail From: Tom Leinster Newsgroups: gmane.science.mathematics.categories Subject: Paper: Euler characteristic as a divergent sum Date: Fri, 06 Jul 2007 16:50:52 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019537 10389 80.91.229.2 (29 Apr 2009 15:38:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:38:57 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Jul 7 08:01:53 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 07 Jul 2007 08:01:53 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I77rW-0003cI-FK for categories-list@mta.ca; Sat, 07 Jul 2007 07:50:02 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 4 Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:3810 Archived-At: The following paper is available: "The Euler characteristic of a category as the sum of a divergent series" The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite, the sum diverges. Nevertheless, it can sometimes be evaluated; in particular, this is possible when the complex is the nerve of a finite category. This provides an alternative definition of the Euler characteristic of a category, which is in many cases equivalent to the original one. http://arxiv.org/abs/0707.0835 Many thanks to Clemens Berger for suggesting the original idea. Best wishes, Tom