Equivariant, locally finite inverse representations with uniformly bounded zipping length, for arbitrary finitely presented groups

TL;DR

This paper establishes a new class of inverse representations for finitely presented groups that are equivariant, locally finite, and have uniformly bounded zipping length, advancing understanding of group representations.

Contribution

It introduces the first detailed proof of inverse representations with specific properties for arbitrary finitely presented groups, expanding the theoretical framework.

Findings

Proves existence of equivariant, locally finite inverse representations

Demonstrates uniformly bounded zipping length for these representations

Provides foundational results for further group representation studies

Abstract

This is the first of a three parts paper providing full details for our previous announcement in Pr\'epublications Orsay 2007-16, arXiv:0711.3579. Here we prove the results stated in the title.