On the groupoid of transformations of rigid structures on surfaces

TL;DR

This paper proves that the groupoid of transformations of rigid structures on surfaces has a finite presentation, confirming a conjecture and exploring applications to TQFTs and connections to the Grothendieck-Teichmuller groupoid.

Contribution

It establishes a finite presentation for the groupoid of transformations of rigid structures on surfaces, confirming a conjecture and providing new insights into related mathematical structures.

Findings

Finite presentation of the groupoid established

Connections to TQFT applications demonstrated

Relation to Grothendieck-Teichmuller groupoid explored

Abstract

We prove that the groupoid of transformations of rigid structures on surfaces has a finite presentation as a 2-groupoid establishing a result first conjectured by G.Moore and N.Seiberg. An alternative proof was given by B.Bakalov and A.Kirillov Jr. We present some applications to TQFTs. This is also related to recent work on the Grothendieck-Teichmuller groupoid by P.Lochak, A.Hatcher and L.Schneps.