Department of Mathematics, Waseda University
Web Page of Jun MURAKAMI
http://www.f.waseda.jp/murakami/
ADDRESS:
Department of Mathematics
Faculty of Fundamental Science and Engineering
Waseda University
3-4-1 Okubo Shinjuku-ku Tokyo, 169-8555 JAPAN
Phone: +81(0)3-5286-3859

RIKO Topology Seminar

T.B.A.

 

What I am working on

I am working on invariants of knots, links and 3-manifolds.

  • Volume conjecture

We propose volume conjecture of knots with Hitoshi Murakami from Kashaev's conjecture, suggesting that the hyperbolic volume of the complement of a hyperbolic knot is determined by the Jones polynomial and its generalizations.

  • Universal perturbative invariant

The universal perturbative invariant of 3-manifolds is constructed with T. T. Q. Le and T. Ohtsuki. I am studying on the representation of the mapping class groups constructed from the Topological Quantum Field Theory of the universal perturbative invariant.

Preprints

The volume formulas for a spherical tetrahedron
arXiv:1011.2584, to appear in Proc. Amer. Math. Soc.

 

On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume, (with Francesco Costantino)
arXiv:1009.3137, to appear in Quantum Topology.

 

Actual computation for the complexified hyperbolic volume conjecture (2002/7/2)

Generalized volume and geometric structure of 3-manifolds (revised on 2002/4/8)

Finite-type invariants detecting the mutant knots
Knot Thoery - Dedicated to Professor Kunio Murasugi for his 70th birthday -
Editors: M. Sakuma et al., Published at Osaka University, March 2000.

On web diagrams

Abstract

In this paper, web diagrams and web spaces are introduced and the construction of the universal perturbative invariant, taking values in the web space, is explained. Applying this invariant to the mapping cylinders of elements of the mapping class group Mg of the surface of genus g, we get web representations of Mg on the web space. The web space has two natural filtrations and these representations are compatible with these filtrations. This fact seems to explain that the representations are not so simple ones.

 

 

Workshop

Volume Conjecture

-- Invariants and geometry of knots --

2010.01.14 -- 01.16

at Waseda University Nishi-waseda Campus
Videos and slides of lectures are available from the following

Workshop archive is here

Copyright (C) Jun Murakami, 2009.