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Logarithmic Hennings invariants for restrictedquantum $sl(2)$


Beliakova, Anna; Blanchet, Christian; Geer, Nathan (2018). Logarithmic Hennings invariants for restrictedquantum $sl(2)$. Algebraic & Geometric Topology, 18(7):4329-4358.

Abstract

We construct a Hennings-type logarithmic invariant for restricted quantum $sl(2)$ at a$2p^{th}$ root of unity. This quantum group $U$ is not quasitriangular and hence not ribbon, but factorizable. The invariant is defined for a pair: a $3–$manifold $M$ and a colored link $L$ inside $M$. The link $L$ is split into two parts colored by central elements and by trace classes, or elements in the $0^{th}$ Hochschild homology of $U$, respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of U, and the modified trace introduced by the third author with his collaborators and computed on tensor powers of the regular representation. Our invariant is a colored extension of the logarithmic invariant constructed by Jun Murakami.

Abstract

We construct a Hennings-type logarithmic invariant for restricted quantum $sl(2)$ at a$2p^{th}$ root of unity. This quantum group $U$ is not quasitriangular and hence not ribbon, but factorizable. The invariant is defined for a pair: a $3–$manifold $M$ and a colored link $L$ inside $M$. The link $L$ is split into two parts colored by central elements and by trace classes, or elements in the $0^{th}$ Hochschild homology of $U$, respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of U, and the modified trace introduced by the third author with his collaborators and computed on tensor powers of the regular representation. Our invariant is a colored extension of the logarithmic invariant constructed by Jun Murakami.

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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Geometry and Topology
Language:English
Date:11 December 2018
Deposited On:17 Jan 2019 09:39
Last Modified:25 Sep 2019 00:06
Publisher:Mathematical Sciences Publishers
ISSN:1472-2739
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.2140/agt.2018.18.4329

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