|Integral TQFT and applications|
|Time：||Wed/Fri 10:10-12:00, 2016-10-19~ 2016-11-11|
|Instructor：||Gregor Masbaum [CNRS, IMJ-PRG, Paris, France]|
|Place：||Conference Room 4, Floor 2, Jin Chun Yuan West Building|
Integral TQFT is an integral refinement of Witten-Reshetikhin-Turaev TQFT defined over a ring of cyclotomic integers. The goalof this lecture series is to give an introduction to Integral TQFTand to discuss some applications to low-dimensional topologyand to mapping class groups. Our main tool in the constructionwill be the skein theory of the Kauffman bracket.
Basic low-dimensional topology.
C. Blanchet, N. Habegger, G. Masbaum, P. Vogel. Topologicalquantum field theories derived from the Kauffman bracket.Topology 34 (1995) 883-927.
G. Masbaum, P. M. Gilmer. Integral Lattices in TQFT. Ann. Sci.École Norm. Sup. 40 (2007) 815-844.
G. Masbaum, A. W. Reid. All finite groups are involved in theMapping Class Group. Geometry & Topology 16 (2012) 1393-1411.
T. Koberda, R. Santharoubane. Quotients of surface groups andhomology of finite covers via quantum representations.Inventiones (to appear), arXiv:1510.00677