Relationship of the Hennings and Chern-Simons Invariants For Higher Rank Quantum Groups

2017/01/05 by Winston Cheong, Alexander Doser, Cheong, Winston +6
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #math.GT #math.QA #msc:17B37 #msc:57M27 #msc:81R50

paper · pdf · doi:10.48550/arxiv.1701.01423

25 pages, 7 figures, heavy hyperref (download TeX and set view counter to adjust contrast for printing/reading with hyperlinks)

arxiv created 2018/07/24 · arxiv updated 2018/07/26

Abstract

The Hennings invariant for the small quantum group associated to an arbitrary simple Lie algebra at a root of unity is shown to agree with Jones- Witten-Reshetikhin-Turaev invariant arising from Chern-Simons filed theory for the same Lie algebra and the same root of unity on all integer homol- ogy three-spheres, at roots of unity where both are defined. This partially generalizes the work of Chen, et al. ([CYZ12, CKS09]) which relates the Hennings and Chern-Simons invariants for SL(2) and SO(3) for arbitrary rational homology three-spheres.

Related

• Quantum invariants of 3-manifolds associated to restricted quantum groups
• Chern-Simons approach to three-manifold invariants
• A quantization of the SL₂(ℂ) Chern-Simons invariant of tangle exteriors
• Chern-Simons Theory, Knot Invariants, Vertex Models and Three-manifold Invariants
• Knot Invariants and Chern-Simons Theory