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Random van Kampen diagrams and algorithmic problems in groups

Random van Kampen diagrams and algorithmic problems in groups In this paper we study the structure of random van Kampen diagrams over finitely presented groups. Such diagrams have many remarkable properties. In particular, we show that a random van Kampen diagram over a given group is hyperbolic, even though the group itself may not be hyperbolic. This allows one to design new fast algorithms for the Word Problem in groups. We introduce and study a new filling function, the depth of van Kampen diagrams, –– a crucial algorithmic characteristic of null-homotopic words in the group. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

Random van Kampen diagrams and algorithmic problems in groups

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Publisher
de Gruyter
Copyright
©© de Gruyter 2011
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/GCC.2011.006
Publisher site
See Article on Publisher Site

Abstract

In this paper we study the structure of random van Kampen diagrams over finitely presented groups. Such diagrams have many remarkable properties. In particular, we show that a random van Kampen diagram over a given group is hyperbolic, even though the group itself may not be hyperbolic. This allows one to design new fast algorithms for the Word Problem in groups. We introduce and study a new filling function, the depth of van Kampen diagrams, –– a crucial algorithmic characteristic of null-homotopic words in the group.

Journal

Groups - Complexity - Cryptology – de Gruyter

Published: May 1, 2011

Keywords: Word problem; finitely presented groups; search algorithms; van Kampen diagram; hyperbolic diagrams; Todd––Coxeter algorithm

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