Volume 21, issue 6 (2021)

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

Volume 21
Issue 7, 3221–3734
Issue 6, 2677–3220
Issue 5, 2141–2676
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

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
Fundamental shadow links realized as links in $S^3$

Sanjay Kumar

Algebraic & Geometric Topology 21 (2021) 3153–3198

We use purely topological tools to construct several infinite families of hyperbolic links in the 3–sphere that satisfy the Turaev–Viro invariant volume conjecture posed by Chen and Yang. To show that our links satisfy the volume conjecture, we prove that each has complement homeomorphic to the complement of a fundamental shadow link. These are links in connected sums of copies of S2 × S1 for which the conjecture is known due to Belletti, Detcherry, Kalfagianni and Yang. Our methods also verify the conjecture for several hyperbolic links with crossing number less than twelve. In addition, we show that every link in the 3–sphere is a sublink of a link that satisfies the conjecture.

As an application of our results, we extend the class of known examples that satisfy the AMU conjecture on quantum representations of surface mapping class groups. For example, we give explicit elements in the mapping class group of a genus g surface with four boundary components for any g. For this, we use techniques developed by Detcherry and Kalfagianni which relate the Turaev–Viro invariant volume conjecture to the AMU conjecture.

fundamental shadow links, Turaev–Viro invariant volume conjecture, AMU conjecture
Mathematical Subject Classification
Primary: 57K31, 57K32, 57M50
Received: 15 June 2020
Revised: 11 October 2020
Accepted: 26 October 2020
Published: 22 November 2021
Sanjay Kumar
Department of Mathematics
Michigan State University
East Lansing, MI
United States