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arXiv · 2302.05529

Renormalized Reshetikhin-Turaev invariants for the unrolled quantum group of $\mathfrak{sl}_2(\mathbb{C})$

Nathan Geer·Adam Robertson·Jan-Luca Spellmann·Matthew B. Young
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Abstract

This paper is a self-contained introduction to the theory of renormalized Reshetikhin-Turaev invariants of links defined by Geer, Patureau-Mirand and Turaev. Whereas the standard Reshetikhin-Turaev theory of a $\mathbb{C}$-linear ribbon category assigns the trivial invariant to any link with a component colored by a simple object of vanishing quantum dimension, the renormalized theory does not. We give a streamlined development of the renormalized Reshetikhin-Turaev theory of links for the category of weight modules over the restricted unrolled quantum group of $\mathfrak{sl}_2(\mathbb{C})$ at an even root of unity.

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Nathan Geer, Adam Robertson, Jan-Luca Spellmann, Matthew B. Young. 2023-02-10. Renormalized Reshetikhin-Turaev invariants for the unrolled quantum group of $\mathfrak{sl}_2(\mathbb{C})$. https://arxiv.org/abs/2302.05529

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