Volume 18, issue 7 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Logarithmic Hennings invariants for restricted quantum ${\mathfrak{sl}}(2)$

Anna Beliakova, Christian Blanchet and Nathan Geer

Algebraic & Geometric Topology 18 (2018) 4329–4358

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.

quantum invariants, links, Hopf algebras, quantum Groups
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 17B37, 57M25
Received: 10 April 2018
Accepted: 7 June 2018
Published: 11 December 2018
Anna Beliakova
Institut für Mathematik
Universität Zürich
Christian Blanchet
Institut de Mathématiques de Jussieu - Paris Rive Gauche
Université Paris 7 (Denis Diderot)
Nathan Geer
Department of Mathematics and Statistics
Utah State University
Logan, UT
United States