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

Louis Funar (1) , Vlad Sergiescu (1)

1 IF - Institut Fourier

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.

Mots clés: Thompson group; Ptolemy groupoid; infinite braid group; quantization; Teichmuller space; braided Thompson group; Euler class; discrete Godbillon-Vey class

Domaines: Topologie géométrique [math.GT]

Louis Funar, Vlad Sergiescu. Central extensions of the Ptolemy-Thompson group and quantized Teichmuller theory. 2008. ⟨hal-00257925v2⟩