Pure and Applied Mathematics Quarterly

Volume 12 (2016)

Number 4

Connected sum of orientable surfaces and Reidemeister torsion

Pages: 517 – 541

DOI: http://dx.doi.org/10.4310/PAMQ.2016.v12.n4.a4

Authors

Esma Dirican (Department of Mathematics, Faculty of Science, Hacettepe University, Ankara, Turkey)

Yaşar Sözen (Department of Mathematics, Faculty of Science, Hacettepe University, Ankara, Turkey)

Abstract

Let $\Sigma_{g,n}$ be an orientable surface with genus g ≥ 2 bordered by $n \geq 1$ 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 $\Sigma_{g,n}$.

Keywords

Reidemeister torsion, symplectic chain complex, homological algebra, orientable surfaces

Full Text (PDF format)

This research was supported by TÜBİTAK (project no. 114F516). The first author would also like to thank TÜBİTAK for the financial support.

Received 24 January 2017