Volume 4 (2002)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989

On the quantum sl2 invariants of knots and integral homology spheres

Kazuo Habiro

Geometry & Topology Monographs 4 (2002) 55–68

DOI: 10.2140/gtm.2002.4.55


We will announce some results on the values of quantum sl2 invariants of knots and integral homology spheres. Lawrence's universal sl2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the quantized enveloping algebra of sl2. 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

Mathematical Subject Classification

Primary: 57M27

Secondary: 17B37


Received: 30 November 2001
Revised: 8 April 2002
Accepted: 22 July 2002
Published: 19 September 2002

Kazuo Habiro
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502