## Tuesday Seminar on Topology

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) KOHNO Toshitake, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya Tea: 16:30 - 17:00 Common Room

### 2022/06/07

17:00-18:00   Online
Pre-registration required. See our seminar webpage.

Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups (JAPANESE)
[ Abstract ]
We discuss a relation between a dynamical zeta function defined by the geodesic flow on a 2-dimensional hyperbolic orbifold and the asymptotic behavior of the Reidemeister torsion for the unit tangent bundle over the orbifold. The unit tangent bundle over a hyperbolic orbifold is a Seifert fibered space with a geometric structure given by the universal cover of PSL(2, R). This geometric structure induces an SL(2, R)-representation of the fundamental group. Here the asymptotic behavior of the Reidemeister torsion means the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle over a hyperbolic orbifold and the SL(n, R)-representations induced by the SL(2, R)-one of its fundamental group. For a hyperbolic 3-manifold, we can derive the hyperbolic volume from the limit of the leading coefficient in the Reidemeister torsion with a dynamical zeta function according to previous works. For the unit tangent bundle over a 2-dimensional hyperbolic orbifold, which is not a hyperbolic 3-manifold, we can find the orbifold Euler characteristic of the orbifold in the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle from the relation with the dynamical zeta function defined by the geodesic flow on the orbifold.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html