Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Center and torsion of a quotient of the group of piecewise linear homeomorphisms of the real line

Swarup Bhowmik

Abstract

In this article, we show that the group comprising piecewise-linear homeomorphisms of the real line with bounded slopes is not simple. Furthermore, we establish that a quotient of this group is torsion-free, and importantly, the center of that quotient group is indeed trivial.

Center and torsion of a quotient of the group of piecewise linear homeomorphisms of the real line

Abstract

In this article, we show that the group comprising piecewise-linear homeomorphisms of the real line with bounded slopes is not simple. Furthermore, we establish that a quotient of this group is torsion-free, and importantly, the center of that quotient group is indeed trivial.
Paper Structure (10 sections, 7 theorems, 8 equations)

This paper contains 10 sections, 7 theorems, 8 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. $PL_\delta$-homeomorphisms of $\mathbb{R}$
  4. Quasi-isometry
  5. Notations
  6. Structure of $PL_\delta(\mathbb{R})$
  7. Algebraic and Geometric properties
  8. Proof of Theorem \ref{['Non-simple']}
  9. Proof of Theorem \ref{['Torsion-free']}
  10. Proof of Theorem \ref{['Center']}

Key Result

Theorem 1.1

The group $PL_\delta^{+}(\mathbb{R})$ (or $PL_\delta([0,+\infty])$) is not simple.

Theorems & Definitions (12)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Definition 2.1
  • Lemma 3.1
  • proof
  • Corollary 3.2
  • Lemma 4.1
  • proof
  • Remark 4.2
  • ...and 2 more