A Projective Representation of the Modular Group

Nadav Kohen; Charles Frohman

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arXiv · 2010.08894

A Projective Representation of the Modular Group

Nadav Kohen·Charles Frohman

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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, $SL_2(\mathbb{Z})$. Also known as the modular group. We use this representation to associate a matrix to each element of $SL_2(\mathbb{Z})$; we then compute the trace and determinant of the associated matrix.

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Nadav Kohen, Charles Frohman. 2020-10-18. A Projective Representation of the Modular Group. https://arxiv.org/abs/2010.08894

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