Curvature testing in 3-dimensional metric polyhedral complexes

Title: Curvature testing in 3-dimensional metric polyhedral complexes
Creator: Elder, Murray; McCammond, Jon
Relation: Experimental Mathematics Vol. 11, Issue 1, p. 143-158
Relation: http://www.emis.de/journals/EM/expmath/volumes/11/11.html
Publisher: A. K. Peters
Resource Type: journal article
Date: 2002
Description: In a previous article, the authors described an algorithm to determine whether a finite metric polyhedral complex satisfied various local curvature conditions such as being locally CAT(0).The proof made use of Tarski’s theorem about the decidability of first order sentences over the reals in an essential way, and thus it was not immediately applicable to a specific finite complex. In this article, we describe an algorithm restricted to 3-dimensional complexes which uses only elementary 3-dimensional geometry. After describing the procedure, we include several examples involving Euclidean tetrahedra which were run using an implementation of the algorithm in GAP
Subject: non-positive curvature; CAT(0)
Identifier: http://hdl.handle.net/1959.13/930995
Identifier: uon:10974
Identifier: ISSN:1058-6458
Language: eng
Full Text
Reviewed

		Thumbnail	File	Description	Size	Format
View Details Download			ATTACHMENT02	Author final version	225 KB	Adobe Acrobat PDF	View Details Download