Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems

TL;DR

This paper introduces a new approach to studying relatively hyperbolic groups using relative isoperimetric inequalities, exploring their geometric, algebraic, and algorithmic properties.

Contribution

It proposes a novel framework based on relative isoperimetric inequalities to analyze various properties of relatively hyperbolic groups.

Findings

Establishes connections between relative isoperimetric inequalities and group properties

Provides new insights into the geometric structure of relatively hyperbolic groups

Discusses implications for algorithms related to these groups

Abstract

We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.