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.
Keywords
quantum invariant, colored Jones
polynomial, universal invariant, Witten-Reshetikhin-Turaev
invariant
