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

Winston Cheong; Alexander Doser; McKinley Gray; Stephen F. Sawin

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arXiv · 1701.01423

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

Winston Cheong·Alexander Doser·McKinley Gray·Stephen F. Sawin

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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.

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Winston Cheong, Alexander Doser, McKinley Gray, Stephen F. Sawin. 2017-01-05. Relationship of the Hennings and Chern-Simons Invariants For Higher Rank Quantum Groups. https://arxiv.org/abs/1701.01423

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