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G^3, Special Session in Geometric Group Theory
January 10-13, 2001
part of the AMS/MAA joint meeting
New Orleans, LA, USA

Organizers
Phil Bowers, Martin Bridson, Stephen Brick, Jon Corson, Igor Mineyev

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An algorithm to detect a nonpositively-curved metric simplicial complex
by
Jon McCammond
Texas A&M University
Coauthors: Murray Elder (Texas A&M University)

A metric simplical complex is a simplicial complex in which constant curvature metrics (with identical curvature constants) have been consistently assigned to each simplex. If such a complex has a metric of nonpositive curvature in the sense of Alexandrov, then a number of consequences about the structure of the fundamental group follow immediately. Unfortunately, there currently exist very few cases where it is possible to determine whether a given finite metric simplicial complex has a metric of nonpositive curvature. In this talk we will discuss recent work with Murray Elder in which we provide such an algorithm using the theory of Groebner bases from computational algebraic geometry.

Date received: September 26, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafm-07.