English

Laplace transform and universal sl(2) invariants

Quantum Algebra 2007-05-23 v1 Commutative Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.math/0509394,
  title  = {Laplace transform and universal sl(2) invariants},
  author = {Anna Beliakova and Christian Blanchet and Thang Le},
  journal= {arXiv preprint arXiv:math/0509394},
  year   = {2007}
}

Comments

21 pages, no figures