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

The central extension of the Thompson group $T$ that arises in the quantized Teichm"uller 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.