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Tuesday Seminar on Topology
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2017/05/16
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Hiroshi Goda (Tokyo University of Agriculture and Technology)
Twisted Alexander invariants and Hyperbolic volume of knots (JAPANESE)
Hiroshi Goda (Tokyo University of Agriculture and Technology)
Twisted Alexander invariants and Hyperbolic volume of knots (JAPANESE)
[ Abstract ]
In [1], Müller investigated the asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, and then Menal-Ferrer and Porti [2] have obtained a formula on the volume of a hyperbolic 3-manifold using the Higher-dimensional Reidemeister torsion.
On the other hand, Yoshikazu Yamaguchi has shown that a relationship between the twisted Alexander polynomial and the Reidemeister torsion associated with the adjoint representation of the holonomy representation of a hyperbolic 3-manifold in his thesis [3].
In this talk, we observe that Yamaguchi's idea is applicable to the Higher-dimensional Reidemeister torsion, then we give a volume formula of a hyperbolic knot using the twisted Alexander polynomial.
References
[1] Müller, W., The asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, Metric and differential geometry, 317--352, Progr. Math., 297, Birkhäuser/Springer, Basel, 2012.
[2] Menal-Ferrer, P. and Porti, J., Higher-dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds. J. Topol., 7 (2014), no. 1, 69--119.
[3] Yamaguchi, Y., On the non-acyclic Reidemeister torsion for knots, Dissertation at the University of Tokyo, 2007.
In [1], Müller investigated the asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, and then Menal-Ferrer and Porti [2] have obtained a formula on the volume of a hyperbolic 3-manifold using the Higher-dimensional Reidemeister torsion.
On the other hand, Yoshikazu Yamaguchi has shown that a relationship between the twisted Alexander polynomial and the Reidemeister torsion associated with the adjoint representation of the holonomy representation of a hyperbolic 3-manifold in his thesis [3].
In this talk, we observe that Yamaguchi's idea is applicable to the Higher-dimensional Reidemeister torsion, then we give a volume formula of a hyperbolic knot using the twisted Alexander polynomial.
References
[1] Müller, W., The asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, Metric and differential geometry, 317--352, Progr. Math., 297, Birkhäuser/Springer, Basel, 2012.
[2] Menal-Ferrer, P. and Porti, J., Higher-dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds. J. Topol., 7 (2014), no. 1, 69--119.
[3] Yamaguchi, Y., On the non-acyclic Reidemeister torsion for knots, Dissertation at the University of Tokyo, 2007.
