Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Divergence functions of higher-dimensional Thompson's groups

Yuya Kodama

Abstract

We prove that higher-dimensional Thompson's groups have linear divergence functions. By the work of Druţu, Mozes, and Sapir, this implies none of the asymptotic cones of $nV$ has a cut-point.

Divergence functions of higher-dimensional Thompson's groups

Abstract

We prove that higher-dimensional Thompson's groups have linear divergence functions. By the work of Druţu, Mozes, and Sapir, this implies none of the asymptotic cones of has a cut-point.
Paper Structure (11 sections, 17 equations, 11 figures)

This paper contains 11 sections, 17 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Definition of higher-dimensional Thompson's groups
  4. Homeomorphisms on the direct product of Cantor sets
  5. Pairs of colored binary trees
  6. Grid diagrams
  7. A generating set of $2V$ and estimations of the word length.
  8. Divergence functions of finitely generated groups
  9. Proof of Theorem \ref{['theorem_divergence_nV']}
  10. Size of the bottom left rectangle
  11. Construction of the path

Figures (11)

  • Figure 1: The trivial pattern, the pattern once divided vertically, the pattern once divided horizontally, and a pattern.
  • Figure 2: A binary tree and a caret.
  • Figure 3: The two types of carets and a colored binary tree obtained from a pattern.
  • Figure 4: Two colored binary trees give the same pattern.
  • Figure 5: A grid pattern.
  • ...and 6 more figures

Theorems & Definitions (10)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof