The Witten-Reshetikhin-Turaev invariant for links in finite order mapping tori I

被引：10

作者：

Andersen, Jorgen Ellegaard ^{[1
]}

Himpel, Benjamin ^{[1
]}

Jorgensen, Soren Fuglede ^{[2
]}

Martens, Johan ^{[3
,4
]}

McLellan, Brendan ^{[5
]}

机构：

[1] Aarhus Univ, Ctr Quantum Geometry Moduli Spaces QGM, Ny Munkegade 118,Bldg 1530, DK-8000 Aarhus C, Denmark

[2] Uppsala Univ, Dept Math, Box 480, SE-75106 Uppsala, Sweden

[3] Univ Edinburgh, Sch Math, Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland

[4] Univ Edinburgh, Maxwell Inst Math Sci, Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland

[5] Harvard Univ, Dept Math, One Oxford St, Cambridge, MA 02138 USA

来源：

ADVANCES IN MATHEMATICS | 2017年 / 304卷

基金：

新加坡国家研究基金会; 瑞典研究理事会;

关键词：

Witten-Reshetikhin-Turaev link; invariants; Chern-Simons theory; TQFT; Gauge theory; Asymptotic expansion conjecture; Growth rate conjecture; STABLE PARABOLIC BUNDLES; CONFORMAL FIELD-THEORY; SIMONS GAUGE-THEORY; MODULI SPACES; VECTOR-BUNDLES; GEOMETRIC-QUANTIZATION; RIEMANNIAN GEOMETRY; SINGULAR-VARIETIES; KAUFFMAN BRACKET; THETA-FUNCTIONS;

D O I：

10.1016/j.aim.2016.08.042

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We state Asymptotic Expansion and Growth Rate conjectures for the Witten-Reshetikhin-Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order automor-phisms of marked surfaces. Our approach is based upon geometric quantisation of the moduli space of parabolic bundles on the surface, which we show coincides with the construction of the Witten-Reshetikhin-Turaev invariants using conformal field theory, as was recently completed by Andersen and Ueno. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：131 / 178

页数：48

共 78 条

[11] [Anonymous], 1993, Internat. J. Math
[12] THE YANG-MILLS EQUATIONS OVER RIEMANN SURFACES
ATIYAH, MF
BOTT, R
[J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1983, 308 (1505): : 523 - 615
[13] SELF-DUALITY IN 4-DIMENSIONAL RIEMANNIAN GEOMETRY
ATIYAH, MF
HITCHIN, NJ
SINGER, IM
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1978, 362 (1711): : 425 - 461
[14] SPECTRAL ASYMMETRY AND RIEMANNIAN GEOMETRY .1.
ATIYAH, MF
PATODI, VK
SINGER, IM
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1975, 77 (JAN) : 43 - 69
[15] Atiyah MF., 1957, Proc. London Math. Soc., V7, P414, DOI 10.1112/plms/s3-7.1.414
[16] AXELROD S, 1991, J DIFFER GEOM, V33, P787
[17] RIEMANN-ROCH AND TOPOLOGICAL K-THEORY FOR SINGULAR-VARIETIES
BAUM, P
FULTON, W
MACPHERSON, R
[J]. ACTA MATHEMATICA, 1979, 143 (3-4) : 155 - 192
[18] LEFSCHETZ-RIEMANN-ROCH FOR SINGULAR-VARIETIES
BAUM, P
FULTON, W
QUART, G
[J]. ACTA MATHEMATICA, 1979, 143 (3-4) : 193 - 211
[19] CONFORMAL BLOCKS AND GENERALIZED THETA-FUNCTIONS
BEAUVILLE, A
LASZLO, Y
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 164 (02) : 385 - 419
[20] Beauville A., 1996, ISAE MARTH COUF P, V9, P75

← 1 2 3 4 5 6 7 8 →