Geodesic
Logarithmic Hennings invariants for restricted quantum 𝔰𝔩(2)
Beliakova, Anna1 ; Blanchet, Christian2 ; Geer, Nathan3
1 Institut für Mathematik, Universität Zürich, Zurich, Switzerland
2 Institut de Mathématiques de Jussieu - Paris Rive Gauche, Université Paris 7 (Denis Diderot), Paris, France
3 Department of Mathematics and Statistics, Utah State University, Logan, UT, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 4329-4358

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2018.18.4329
Classification : 57M27, 17B37, 57M25
Keywords: quantum invariants, links, Hopf algebras, quantum Groups

Beliakova, Anna 1 ; Blanchet, Christian 2 ; Geer, Nathan 3

1 Institut für Mathematik, Universität Zürich, Zurich, Switzerland
2 Institut de Mathématiques de Jussieu - Paris Rive Gauche, Université Paris 7 (Denis Diderot), Paris, France
3 Department of Mathematics and Statistics, Utah State University, Logan, UT, United States 
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     author = {Beliakova, Anna and Blanchet, Christian and Geer, Nathan},
     title = {Logarithmic {Hennings} invariants for restricted quantum \ensuremath{\mathfrak{s}}\ensuremath{\mathfrak{l}}(2)},
     journal = {Algebraic and Geometric Topology},
     pages = {4329--4358},
     publisher = {mathdoc},
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     doi = {10.2140/agt.2018.18.4329},
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Beliakova, Anna; Blanchet, Christian; Geer, Nathan. Logarithmic Hennings invariants for restricted quantum 𝔰𝔩(2). Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 4329-4358. doi: 10.2140/agt.2018.18.4329

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