Presentations of higher dimensional Thompson groups

Abstract

In a previous paper, we defined a higher dimensional analog of Thompson's group V, and proved that it is simple, infinite, finitely generated, and not isomorphic to any of the known Thompson groups. There are other Thompson groups that are infinite, simple and finitely presented. Here we show that the new group is also finitely presented by calculating an explicit finite presentation.

35 pages, to appear in J. Algebra

References in corpus (3)

• Higher Dimensional Thompson Groups
• On the Zappa-Szep Product
• The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand

Cited by in corpus (14)

• On the Baker's map and the Simplicity of the Higher Dimensional Thompson Groups nV
• The Brin-Thompson groups sV are of type F_\infty
• Twisted Brin-Thompson groups
• Etale groupoids arising from products of shifts of finite type
• Permutation-based presentations for Brin's higher-dimensional Thompson groups $nV$
• Higher dimensional Thompson groups have Serre's property FA
• Presentations for the higher dimensional Thompson's groups nV
• The word problem of the Brin-Higman-Thompson groups
• A monoid version of the Brin-Higman-Thompson groups
• Metric properties of higher-dimensional Thompson's groups
• Cohomological finiteness properties of the Brin-Thompson-Higman groups 2V and 3V
• Divergence functions of higher-dimensional Thompson's groups
• A Description of Aut(dVn) and Out(dVn) Using Transducers
• The word problem of the Brin-Thompson group is coNP-complete