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On a small cancellation theorem of Gromov

Yann Ollivier

Abstract

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from labelled graphs.

On a small cancellation theorem of Gromov

Abstract

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from labelled graphs.

Paper Structure

This paper contains 5 sections, 7 theorems, 2 equations.

Table of Contents

  1. Statement and discussion
  2. Acknowledgements.
  3. Idea of proof
  4. Proof (expanded version)
  5. Further remarks

Key Result

Theorem 1

Let $\Gamma$ be a finite reduced non-filamenteous labelled graph. Let $R$ be the set of words read on all cycles of $\Gamma$ (or on a generating family of cycles). Let $g$ be the girth of $\Gamma$ and $\Lambda$ be the length of the longest piece of $\Gamma$. If $\Lambda<g/6$ then the presentation $\

Theorems & Definitions (26)

  • Theorem 1: (M. Gromov, G3)
  • Remark 2
  • Remark 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • proof : Proof of the theorem.
  • ...and 16 more