2002/11/04 by Kazuo Habiro · 1 citation
Mathematics · #math.GT #math.QA #msc:57M27 #msc:17B37
published as Geom. Topol. Monogr. 4 (2002) 55-68 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper5.abs.html
arxiv created 2002/11/04 · arxiv updated 2009/11/30
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.