Geometric presentations for Thompson's groups

Abstract

We prove that Thompson's groups $F$ and $V$ are the geometry groups of associativity, and of associativity together with commutativity, respectively. We deduce new presentations of $F$ and $V$. These presentations lead to considering a certain subgroup of $V$ and an extension of this subgroup. We prove that the latter are the geometry groups of associativity together with the law $x(yz)=y(xz)$, and of associativity together with a twisted version of this law involving self-distributivity, respectively.

References in corpus (2)

• Globalization of Confluent Partial Actions on Topological and Metric Spaces
• The group of parenthesized braids