Date of Submission

Spring 2018

Academic Programs and Concentrations

Computer Science; Mathematics

Project Advisor 1

James Belk

Project Advisor 2

Robert McGrail

Abstract/Artist's Statement

We describe an implementation of the solution to the conjugacy problem in Thompson's group V as presented by James Belk and Francesco Matucci in 2013. Thompson's group V is an infinite finitely presented group whose elements are complete binary prefix replacement maps. From these we can construct closed abstract strand diagrams, which are certain directed graphs with a rotation system and an associated cohomology class. The algorithm checks for conjugacy by constructing and comparing these graphs together with their cohomology classes. We provide a complete outline of our solution algorithm, as well as a description of the data structures which store closed abstract strand diagrams and contain methods to simplify and compare them. The final conjugacy checking program runs in cubic time.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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