Laplace transform and universal sl(2) invariants

Details Laplace transform and universal sl(2) invariants Laplace transform and universal sl(2) invariants

2005-09-18

arxiv.org/abs/math/0509394v1

Mathematics

Quantum Algebra

21 pages, no figures

Scientific paper

We develop a Laplace transform method for constructing universal invariants of 3-manifolds. As an application, we recover Habiro's theory of integer homology 3-spheres and extend it to some classes of rational homology 3-spheres with cyclic homology. If |H_1|=2, we give explicit formulas for universal invariants dominating the sl(2) and SO(3) Witten--Reshetikhin--Turaev invariants, as well as their spin and cohomological refinements at all roots of unity. New results on the Ohtsuki series and the integrality of quantum invariants are the main applications of our construction.

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