A Projective Representation of the Modular Group

2020/10/18 by Kohen, Nadav, Frohman, Charles · 1 citation
#57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2010.08894

Abstract

Quantum Teichmuller theory assigns invariants to three-manifolds via projective representations of mapping class groups derived from the representation of a noncommutative torus. Here, we focus on a representation of the simplest non-commutative torus which remains fixed by all elements of the mapping class group of the torus, SL₂(ℤ). Also known as the modular group. We use this representation to associate a matrix to each element of SL₂(ℤ); we then compute the trace and determinant of the associated matrix.

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• Classical and Quantum Algorithms for Topological Invariants of Torus Bundles

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