Volume 4 (2002)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
 
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN 1464-8997 (online)
ISSN 1464-8989 (print)
 
MSP Books and Monographs
Other MSP Publications

Quantum invariants of Seifert 3–manifolds and their asymptotic expansions

Soren Kold Hansen and Toshie Takata

Geometry & Topology Monographs 4 (2002) 69–87

DOI: 10.2140/gtm.2002.4.69

Abstract

We report on recent results of the authors concerning calculations of quantum invariants of Seifert 3–manifolds. These results include a derivation of the Reshetikhin–Turaev invariants of all oriented Seifert manifolds associated with an arbitrary complex finite dimensional simple Lie algebra, and a determination of the asymptotic expansions of these invariants for lens spaces. Our results are in agreement with the asymptotic expansion conjecture due to J. E. Andersen.

Keywords

quantum invariants, Seifert manifolds, modular categories, quantum groups, asymptotic expansions

Mathematical Subject Classification

Primary: 57M27

Secondary: 17B37, 18D10, 41A60

References
Publication

Received: 3 December 2001
Accepted: 22 July 2002
Published: 19 September 2002

Authors
Soren Kold Hansen
School of Mathematics
University of Edinburgh
JCMB
King's Buildings
Edinburgh EH9 3JZ
UK
Toshie Takata
Department of Mathematics
Faculty of Science
Niigata University
Niigata 950-2181
Japan