Central extensions of the Ptolemy-Thompson group and quantized Teichmuller theory

Abstract

The central extension of the Thompson group $T$ that arises in the quantized Teichmüller theory is 12 times the Euler class. This extension is obtained by taking a (partial) abelianization of the so-called braided Ptolemy-Thompson group introduced and studied in \cite{FK2}. We describe then the cyclic central extensions of $T$ by means of explicit presentations.

26 p

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Cited by in corpus (8)

• Dynamics for holographic codes
• The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization
• Quantum fields for unitary representations of Thompson's groups F and T
• Phase constants in the Fock-Goncharov quantum cluster varieties
• Three-dimensional quantum gravity from the quantum pseudo-Kähler plane
• Phase constants in the Fock-Goncharov quantization of cluster varieties: long version
• Irreducible self-adjoint representations of quantum Teichmüller space and the phase constants
• A note on stable commutator length in braided Ptolemy-Thompson groups