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2018 Logarithmic Hennings invariants for restricted quantum ${\mathfrak{sl}}(2)$
Anna Beliakova, Christian Blanchet, Nathan Geer
Algebr. Geom. Topol. 18(7): 4329-4358 (2018). DOI: 10.2140/agt.2018.18.4329

Abstract

We construct a Hennings-type logarithmic invariant for restricted quantum s l ( 2 ) at a  2 p  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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Anna Beliakova. Christian Blanchet. Nathan Geer. "Logarithmic Hennings invariants for restricted quantum ${\mathfrak{sl}}(2)$." Algebr. Geom. Topol. 18 (7) 4329 - 4358, 2018. https://doi.org/10.2140/agt.2018.18.4329

Information

Received: 10 April 2018; Accepted: 7 June 2018; Published: 2018
First available in Project Euclid: 18 December 2018

zbMATH: 07006393
MathSciNet: MR3892247
Digital Object Identifier: 10.2140/agt.2018.18.4329

Subjects:
Primary: 57M27
Secondary: 17B37, 57M25

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 7 • 2018
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