La propriete de decroissance rapide pour le groupe de Wise

TL;DR

This paper proves that the group introduced by D. Wise possesses the property of rapid decay, a significant feature in geometric group theory, by analyzing its presentation and algebraic properties.

Contribution

It establishes the rapid decay property for Wise's group, providing new insights into its geometric and algebraic structure.

Findings

Wise's group has the property of rapid decay.

The proof involves analyzing the group's presentation and algebraic relations.

This result advances understanding of geometric group properties.

Abstract

We show that the group of presentation $< a,b,c,s,t\mid c=ab=ba,\, c^2=sas^{-1}=tbt^{-1}>$ (introduced by D. Wise) has the property of rapid decay.