Integral TQFT for a one-holed torus

Abstract

We give new explicit formulas for the representations of the mapping class group of a genus one surface with one boundary component which arise from Integral TQFT. Our formulas allow one to compute the h-adic expansion of the TQFT-matrix associated to a mapping class in a straightforward way. Truncating the h-adic expansion gives an approximation of the representation by representations into finite groups. As a special case, we study the induced representations over finite fields and identify them up to isomorphism. The key technical ingredient of the paper are new bases of the Integral TQFT modules which are orthogonal with respect to the Hopf pairing. We construct these orthogonal bases in arbitrary genus, and briefly describe some other applications of them.

18 pages, 8 figures. version 3: Minor expository changes. Bibliography updated

References in corpus (2)

• Congruence and similarity of 3-manifolds
• Heegaard genus, cut number, weak p-congruence, and quantum invariants

Cited by in corpus (4)

• Quotients of surface groups and homology of finite covers via quantum representations
• An application of TQFT to modular representation theory
• Dimension formulas for some modular representations of the symplectic group in the natural characteristic
• On TQFT representations of mapping class groups with boundary