Tuesday Seminar on Topology

[Japanese]   [Past Programs]
This is an online seminar on Zoom.

Last updated September 15, 2021
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Nariya Kawazumi
Takahiro Kitayama
Takuya Sakasai

Pre-registration is required.
Once you register, you can attend all our seminars until the end of March, 2022.

October 5, 17:00-18:00 -- Online on Zoom. Pre-registration required.

Hiroshi Goda (Tokyo University of Agriculture and Technology)

Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds

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.)

October 12, 17:00-18:00 -- Online on Zoom. Pre-registration required.

Nobuo Iida (The Univesity of Tokyo)

Seiberg-Witten Floer homotopy and contact structures

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).