Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories

In this paper we construct invariants of 3-manifolds "\`a la Reshetikhin-Turaev" in the setting of non-semi-simple ribbon tensor categories. We give concrete examples of such categories which lead to a family of 3-manifold invariants indexed by the integers. We prove this family of invariants has several notable features, including: they can be computed via a set of axioms, they distinguish homotopically equivalent manifolds that the standard Reshetikhin-Turaev-Witten invariants do not, and they allow the statement of a version of the Volume Conjecture and a proof of this conjecture for an infinite class of links.Comment: 46 pages, 45 figures, new introduction, some misprints corrected and an example detailed. An appendix added to correct a proo

Etingof-Kazhdan quantization of Lie superbialgebras

For every semi-simple Lie algebra one can construct the Drinfeld-Jimbo algebra U. This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U, Drinfeld used the KZ-equations to construct a quasi-Hopf algebra A. He proved that particular categories of modules over the algebras U and A are tensor equivalent. Analogous constructions of the algebras U and A exist in the case of Lie superalgebra of type A-G. However, Drinfeld's proof of the above equivalence of categories does not generalize to Lie superalgebras. In this paper, we will discuss an alternate proof for Lie superalgebras of type A-G. Our proof utilizes the Etingof-Kazhdan quantization of Lie (super)bialgebras. It should be mentioned that the above equivalence is very useful. For example, it has been used in knot theory to relate quantum group invariants and the Kontsevich integral.Comment: Minor corrections are fixed and Section 4 is simplified as called for by the referee. To appear in Advances in Mathematic

Searching for Antiproton Decay at the Fermilab Antiproton Accumulator

This paper describes an experimental search for antiproton decay at the Fermilab Antiproton Accumulator. The E868 (APEX) experimental setup is described. The APEX data is expected to be sensitive to antiproton decay if the antiproton lifetimes is less than a few times 100 000 years.Comment: http://fnapx1.fnal.gov/talks/eps_preprint.p

On invariants of graphs related to quantum sl(2)\mathfrak{sl}(2) at roots of unity

We show how to define invariants of graphs related to quantum $\mathfrak{sl}(2)$ when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions