Waseda Riko Topology Seminor
Higher genus tangle categories
(Universite de Strasbourg)
Date: December 5 (Thu.) 16:30 ~
Place: Waseda University, Nishi-Waseda Campus, 51st Building, 17th floor, Room 17-06
Volume conjecture of knotted graph
(Korea Institute for Advanced Study)
Date: December 10 (Tue.) 16:30 ~
Place: Waseda University, Hishi-Saseda Campus, 51st Buliding, 18th floor, Room 18-06
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.
Recent papers and preprints
- Volume of a doubly truncated hyperbolic tetrahedron (with Alexander Kolpakov)
arXiv:1203.1061, Aequationes Mathematicae, 2012
- The volume formulas for a spherical tetrahedron
Proc. Amer. Math. Soc. . 140 (2012), no. 9, 3289-3295.
- On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume, (with Francesco Costantino)
Quantum Topology, 4 (2013), no.3, 303-351.
- 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.
- List of my papers
.... errata ....
Copyright (C) Jun Murakami, 2013.