Journal of the Korean Mathematical Society (대한수학회지)

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REIDEMEISTER TORSION AND ORIENTABLE PUNCTURED SURFACES

  • Dirican, Esma (Department of Mathematics IzmIr Institute of Technology) ;
  • Sozen, Yasar (Department of Mathematics Hacettepe University)
  • Received : 2017.09.12
  • Accepted : 2017.11.30
  • Published : 2018.07.01
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Abstract

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.

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References

  1. W. Franz, Uber die Torsion einer Uberdeckung, J. Reine Angew. Math. 173 (1935), 245-254.
  2. J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358-426. https://doi.org/10.1090/S0002-9904-1966-11484-2
  3. C. Ozel and Y. Sozen, Reidemeister torsion of product manifolds and its applications to quantum entanglement, Balkan J. Geom. Appl. 17 (2012), no. 2, 66-76.
  4. J. Porti, Torsion de Reidemeister pour les varietes hyperboliques, Mem. Amer. Math. Soc. 128 (1997), no. 612, x+139 pp.
  5. K. Reidemeister, Homotopieringe und Linsenraume, Abh. Math. Sem. Univ. Hamburg 11 (1935), no. 1, 102-109. https://doi.org/10.1007/BF02940717
  6. Y. Sozen, Reidemeister torsion of a symplectic complex, Osaka J. Math. 45 (2008), no. 1, 1-39.
  7. Y. Sozen, A note on Reidemeister torsion and period matrix of Riemann surfaces, Math. Slovaca 61 (2011), no. 1, 29-38.
  8. Y. Sozen, Symplectic chain complex and Reidemeister torsion of compact manifolds, Math. Scand. 111 (2012), no. 1, 65-91. https://doi.org/10.7146/math.scand.a-15214
  9. Y. Sozen, On a volume element of a Hitchin component, Fund. Math. 217 (2012), no. 3, 249-264. https://doi.org/10.4064/fm217-3-4
  10. Y. Sozen, On Fubini-Study form and Reidemeister torsion, Topology Appl. 156 (2009), no. 5, 951-955. https://doi.org/10.1016/j.topol.2008.10.019
  11. V. Turaev, Torsions of 3-manifolds, in Invariants of knots and 3-manifolds (Kyoto, 2001), 295-302, Geom. Topol. Monogr., 4, Geom. Topol. Publ., Coventry.
  12. E. Witten, On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991), no. 1, 153-209. https://doi.org/10.1007/BF02100009

Cited by

  1. A note on exceptional groups and Reidemeister torsion vol.59, pp.8, 2018, https://doi.org/10.1063/1.5021318