Reidemeister-Franz Torsion of Compact Orientable Surfaces via Pants Decomposition

Abstract

Let ${\Sigma }_{g,n}$ denote the compact orientable surface with genus $g\ge 2$ 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.

12 pages, 2 figures. Some references added