Date of Submission
Academic Programs and Concentrations
Computer Science; Mathematics
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Project Advisor 2
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.
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Nalecz, Rachel K., "An Implementation of the Solution to the Conjugacy Problem on Thompson's Group V" (2018). Senior Projects Spring 2018. 313.