Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 5, pages 55--68.
On the quantum sl_2 invariants of knots and integral homology spheres
We will announce some results on the values of quantum sl_2 invariants
of knots and integral homology spheres. Lawrence's universal sl_2
invariant of knots takes values in a fairly small subalgebra of the
center of the h-adic version of the quantized enveloping algebra of
sl_2. This implies an integrality result on the colored Jones
polynomials of a knot. We define an invariant of integral homology
spheres with values in a completion of the Laurent polynomial ring of
one variable over the integers which specializes at roots of unity to
the Witten-Reshetikhin-Turaev invariants. The definition of our
invariant provides a new definition of Witten-Reshetikhin-Turaev
invariant of integral homology spheres.
Quantum invariant, colored Jones polynomial, universal invariant, Witten-Reshetikhin-Turaev invariant
AMS subject classification.
Submitted to GT on 30 November 2001.
(Revised 8 April 2002.)
Paper accepted 22 July 2002.
Paper published 19 September 2002.
Notes on file formats
Research Institute for Mathematical Sciences
Kyoto University, Kyoto, 606-8502, Japan
GTM home page
These pages are not updated anymore.
They reflect the state of
For the current production of this journal, please refer to