Connected sum of orientable surfaces and Reidemeister torsion


Dirican E., SÖZEN Y.

PURE AND APPLIED MATHEMATICS QUARTERLY, vol.12, no.4, pp.517-541, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.4310/pamq.2016.v12.n4.a4
  • Journal Name: PURE AND APPLIED MATHEMATICS QUARTERLY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.517-541

Abstract

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).