REIDEMEISTER TORSION AND ORIENTABLE PUNCTURED SURFACES

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