951 research outputs found
On the unification of quantum 3-manifold invariants
In 2006 Habiro initiated a construction of generating functions for
Witten-Reshetikhin-Turaev (WRT) invariants known as unified WRT invariants. In
a series of papers together with Irmgard Buehler and Christian Blanchet we
extended his construction to a larger class of 3-manifolds. The unified
invariants provide a strong tool to study properties of the whole collection of
WRT invariants, e.g. their integrality, and hence, their categorification. In
this paper we give a survey on ideas and techniques used in the construction of
the unified invariants.Comment: 18 page
The Colored Jones Polynomial and the A-Polynomial of Knots
We study relationships between the colored Jones polynomial and the
A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ
conjecture (of Garoufalidis) that relates the colored Jones polynomial and the
A-polynomial. Along the way we also calculate the Kauffman bracket skein module
of all 2-bridge knots. Some properties of the colored Jones polynomial of
alternating knots are established.Comment: Typos and minor mistakes corrected. To appear in Advances in
Mathematic
On Denominators of the Kontsevich Integral and the Universal Perturbative Invariant of 3-Manifolds
The integrality of the Kontsevich integral and perturbative invariants is
discussed. We show that the denominator of the degree part of the
Kontsevich integral of any knot or link is a divisor of .
We also show that the denominator of of the degree part of the universal
perturbative invariant of homology 3-spheres is not divisible by any prime
greater than .Comment: 27 pages, LaTeX with graphics packag
Quantum Invariants of Periodic Links and Periodic 3-Manifolds
We give criteria for framed links and 3-manifolds to be periodic of prime
order. As applications we show that the Poincare sphere is of periodicity 2, 3,
5 only and the Brieskorn sphere (2,3,7) is of periodicity 2, 3, 7 only.Comment: 18 pages with 1 figur
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