Toshie Takata

Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links

R. M. Kashaev conjectured that the asymptotic behavior of the link invariant he introduced [Kashaev 951, which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volume of any hyperbolic link complement. We observe numerically that for knots 63, 89 and 820 and for the Whitehead link, the colored Jones polynomials are related to the hyperbolic volumes and the Chern-Simons invariants and propose a complexification of Kashaevs conjecture.

RESHETIKHIN–TURAEV INVARIANTS OF SEIFERT 3-MANIFOLDS FOR CLASSICAL SIMPLE LIE ALGEBRAS

We derive formulas for the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra

A Formula for the Colored Jones Polynomial of 2-Bridge Knots

\mathfrak g

On the set of the logarithm of the LMO invariant for integral homology 3-spheres

in terms of the Seifert invariants and standard data for

Symmetry of Witten’s 3-manifold invariants for sl(n, C)

\mathfrak g

The colored Jones polynomial and the A-polynomial for twist knots

. A main corollary is a determination of the full asymptotic expansions of these invariants for lens spaces in the limit of large quantum level. Our results are in agreement with the asymptotic expansion conjecture due to J. E. Andersen.

On quantum PSU(n) invariants for seifert manifolds

We derive a formula for the colored Jones polynomial of 2-bridge knots. For a twist knot, a more explicit formula is given and it leads to a relation between the degree of the colored Jones polynomial and the crossing number.

Quantum invariants of Seifert 3-manifolds and their asymptotic expansions

The LMO invariant is a very strong invariant such that it is expected to classify integral homology 3-spheres. In this paper we identify the set of the degree = 6 parts of the logarithm of the LMO invariant for integral homology 3-spheres. As an application, we obtain a complete set of relations which characterize the set of Ohtsukis invariants {?i(M)} for i = 6. For any simple Lie algebra , we also obtain a complete set of relations which characterize the set of perturbative P invariants {(M)} for i = 3.