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arXiv · 2403.02562

Grid diagrams for higher-dimensional Thompson's groups

José Burillo·Sean Cleary·Brita Nucinkis
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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.

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José Burillo, Sean Cleary, Brita Nucinkis. 2024-03-05. Grid diagrams for higher-dimensional Thompson's groups. https://arxiv.org/abs/2403.02562

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