Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

3
The categories of this paper are: physics
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat