Reidemeister torsion and orientable punctured surfaces

Abstract

Let Σg,n,b denote the orientable surface obtained from the closed orientable surface Σg of genus g ≥ 2 by deleting the interior of n ≥ 1 distinct topological disks and b ≥ 1 points. Using the notion of symplectic chain complex, the present paper establishes a formula for computing Reidemeister torsion of the surface Σg,n,b in terms of Reidemeister torsion of the closed surface Σg, Reidemeister torsion of disk, and Reidemeister torsion of punctured disk.