Volume 15, issue 4 (2015)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Braids, complex volume and cluster algebras

Kazuhiro Hikami and Rei Inoue

Algebraic & Geometric Topology 15 (2015) 2175–2194
Abstract

We try to give a cluster-algebraic interpretation of the complex volume of knots. We construct the R–operator from cluster mutations, and show that it can be regarded as a hyperbolic octahedron. The cluster variables are interpreted as the edge parameters used by Zickert for computing complex volume.

Keywords
knot, hyperbolic volume, complex volume, cluster algebra
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 13F60
References
Publication
Received: 28 April 2014
Revised: 6 November 2014
Accepted: 14 November 2014
Published: 10 September 2015
Authors
Kazuhiro Hikami
Faculty of Mathematics
Kyushu University
Fukuoka 819-0395
Japan
Rei Inoue
Department of Mathematics and Informatics, Faculty of Science
Chiba University
Chiba 263-8522
Japan