Journal of the
Korean Mathematical Society JKMS

Let $\Sigma_{g,n,b}$ denote the orientable surface obtained from the closed orientable surface $\Sigma_g$ of genus $g\geq2$ 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.

Keywords: Reidemeister torsion, symplectic chain complex, orientable punctured surfaces

MSC numbers: Primary 55U99; Secondary 18G99, 57Q10