Grid diagrams for higher-dimensional Thompson’s groups
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...
| Authors: | , , |
|---|---|
| Format: | article |
| Publication Date: | 2026 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:dnet:upcommonspor::8243779b2427bf57958571528088fb49 |
| Online Access: | https://hdl.handle.net/2117/462256 https://dx.doi.org/10.1017/S0305004126102047 |
| Access Level: | Open access |
| Keyword: | Finite groups Infinite groups Geometric group theory Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| Summary: | 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. |
|---|