Modular functors are determined by their genus zero data

被引：21

作者：

Andersen, Jorgen Ellegaard ^{[1
]}

Ueno, Kenji ^{[2
]}

机构：

[1] Univ Aarhus, Ctr Quantum Geometry Moduli Spaces, DK-8000 Aarhus, Denmark

[2] Hosei Univ, Dept Ind & Syst Engn, Fac Sci & Engn, Koganei, Tokyo 1840002, Japan

来源：

QUANTUM TOPOLOGY | 2012年 / 3卷 / 3-4期

基金：

日本学术振兴会; 新加坡国家研究基金会;

关键词：

Topological quantum field theory; modular functors; curve operators; mapping class groups;

D O I：

10.4171/QT/29

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove in this paper that the genus zero data of a modular functor determines the modular functor. We do this by establishing that the S-matrix in genus one with one point labeled arbitrarily can be expressed in terms of the genus zero information and we give an explicit formula. We do not assume the modular functor in question has duality or is unitary, in order to establish this.

引用

页码：255 / 291

页数：37

共 30 条

[1] Andersen J. E., 2009, TRAVAUX MATH, P167
[2] Andersen J. E., 2007, ARXIV07062184V1
[3] Andersen J. E., 2011, CLAY MATH P
[4] Andersen J. E., 1995, J REINE ANGEW MATH
[5] Andersen J. E., 2011, ARXIV11105027V1
[6] Andersen J. E., MATH P CAMBRIDGE PHI, V141, P477
[7] The Nielsen-Thurston classification of mapping classes is determined by TQFT
Andersen, Jorgen Ellegaard
[J]. JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2008, 48 (02): : 323 - 338
[8] Abelian conformal field theory and determinant bundles
Andersen, Jorgen Ellegaard
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2007, 18 (08) : 919 - 993
[9] Geometric construction of modular functors from conformal field theory
Andersen, Jorgen Ellegaard
Ueno, Kenji
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2007, 16 (02) : 127 - 202
[10] Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups
Andersen, Jorgen Ellegaard
[J]. ANNALS OF MATHEMATICS, 2006, 163 (01) : 347 - 368

← 1 2 3 →