## 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

Future seminars

### 2021/10/05

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Hiroshi Goda (Tokyo University of Agriculture and Technology)
Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds (JAPANESE)
[ Abstract ]
We discuss a relationship between the chirality of knots and higher dimensional twisted Alexander polynomials associated with holonomy representations of hyperbolic $3$-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic $3$-cone-manifold of finite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist knots, according to our criterion, using low-dimensional irreducible representations. (This is a joint work with Takayuki Morifuji.)
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2021/10/12

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Nobuo Iida (The Univesity of Tokyo)
Seiberg-Witten Floer homotopy and contact structures (JAPANESE)
[ Abstract ]
Seiberg-Witten theory has been an efficient tool to study 4-dimensional symplectic and 3-dimensional contact geometry. In this talk, we introduce new homotopical invariants related to these structures using Seiberg-Witten theory and explain their properties and applications. These invariants have two main origins:
1. Kronheimer-Mrowka's invariant for 4-manifold with contact boundary, whose construction is based on Seiberg-Witten equation on 4-manifolds with conical end.
2. Bauer-Furuta and Manolescu's homotopical method called finite dimensional approximation in Seiberg-Witten theory.
This talk includes joint works with Masaki Taniguchi(RIKEN) and Anubhav Mukherjee(Georgia tech).
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html