PURE AND APPLIED MATHEMATICS QUARTERLY, vol.12, no.4, pp.517-541, 2016 (Peer-Reviewed Journal)
Let Sigma(g,n) be an orientable surface with genus g >= 2 bordered by n >= 1 curves homeomorphic to circle. As is well known that one-holed torus Sigma(1,1) is the building block of such surfaces. By using the notion of symplectic chain complex, homological algebra techniques and considering the double of the building block, the present paper proves a novel formula for computing Reidemeister torsion of one-holed torus. Moreover, applying this result and considering Sigma(g,n) as the connected sum Sigma(1,n) #(g - 1)Sigma(1,0), the present paper establishes a novel formula to compute Reidemeister torsion of Sigma(g,n).