Grid diagrams for higher-dimensional Thompson’s groups
Abstract
Abstract We describe standard forms for elements of the higher-dimensional Thompson groups nV arising from gridding subdivision processes. These processes lead to standard normal form descriptions for elements in these groups, and sizes of these standard forms estimate the word length with respect to finite generating sets. These gridded forms lead to standard algebraic descriptions as well, with respect to the both infinite and finite generating sets for these groups.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Advanced Operator Algebra Research
Publication details
- Journal / source
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 181
- Issue
- 2
- Pages
- 1079–1094
- Publication date
- 23 April 2026
- Language
- EN