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...

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Bibliographic Details
Authors: Burillo Puig, José|||0000-0002-1078-3614, Cleary, Sean, Nucinkis, Brita
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
Description
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.