Integral Lattices in TQFT

Abstract

We find explicit bases for naturally defined lattices over a ring of algebraic integers in the SO(3) TQFT-modules of surfaces at roots of unity of odd prime order. Some applications relating quantum invariants to classical 3-manifold topology are given.

31 pages, v2: minor modifications. To appear in Ann. Sci. Ecole Norm. Sup

References in corpus (4)

• The co-rank conjecture for 3-manifold groups
• On the Cut Number of a 3-manifold
• Almost integral TQFTs from simple Lie algebras
• On certain integral tensor categories and integral TQFTs

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• Dimension formulas for some modular representations of the symplectic group in the natural characteristic
• Profinite completions of Burnside-type quotients of surface groups
• Heegaard genus, cut number, weak p-congruence, and quantum invariants
• Homological Construction of Quantum Representations of Mapping Class Groups
• An embedding of skein algebras of surfaces into quantum tori from Dehn-Thurston coordinates
• Arithmetic Groups (Banff, Alberta, April 14-19, 2013)
• Rigidity of Fibonacci representations of mapping class groups
• On modular group representations associated to SO$(p{)}_2$-TQFTs
• On the Turaev-Viro endomorphism, and the colored Jones polynomial
• On the unification of quantum 3-manifold invariants