Reidemeister-Franz Torsion of Compact Orientable Surfaces via Pants Decomposition

TL;DR

This paper derives a formula for Reidemeister torsion of compact orientable surfaces with boundary, using pants decompositions to relate the torsion of the surface to that of simpler pairs of pants.

Contribution

It introduces a novel method to compute Reidemeister torsion of surfaces via pants decomposition, linking global torsion to local pair-of-pants torsions.

Findings

Provides an explicit formula for Reidemeister torsion of $oldsymbol{ ext{Σ}_{g,n}}$

Expresses surface torsion in terms of pair-of-pants torsions

Facilitates calculations of torsion for complex surfaces

Abstract

Let $\Sigma_{g,n}$ denote the compact orientable surface with genus $g\geq 2$ and boundary disjoint union of $n$ circles. By using a particular pants-decomposition of $\Sigma_{g,n},$ we obtain a formula that computes the Reidemeister torsion of $\Sigma_{g,n}$ in terms of Reidemeister torsions of pairs of pants.