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Triangles, Squares and Geodesics by Levitt, Rena; McCammond, Jon is a scholarly article available to read on EtoBox.

What is Triangles, Squares and Geodesics about?

In the early 1990s Steve Gersten and Hamish Short proved that compact nonpositively curved triangle complexes have biautomatic fundamental groups and that compact nonpositively curved square complexes have biautomatic fundamental groups. In this article we report on the extent to which results such as these extend to nonpositively curved complexes built out a mixture of triangles and squares. Since both results by Gersten and Short have been generalized to higher dimensions, this can be viewed as a first step towards unifying Januszkiewicz and {\'S}wi{\.a}tkowski's theory of simplicial nonpositive curvature with the theory of nonpositively curved cube complexes.

Author

Levitt, Rena; McCammond, Jon

Published

2009

Language

EN