|Speaker:||Hyun Kyu Kim (KIAS)|
|Title:||Central extensions of the Ptolemy-Thompson group T from quantization of universal Teichmuller space|
|Date:||Wed, Oct 15, 2014, 16:00 - 17:30|
|Place:||Seminar Room B|
Quantization of the Teichmuller space of a Riemann surface yields projective representations of the mapping class group of the surface, and hence central extensions of it. Quantization of universal Teichmuller space yields central extensions of the Ptolemy-Thompson group, which is a discrete universal analog of mapping class groups, and which is isomorphic to Richard Thompson's group T. Meanwhile, the braided Ptolemy-Thompson groups are extensions of T by the infinite braid group, and by abelianizing the infinite braid group one obtains central extensions of T. We show that these central extensions are isomorphic to the ones coming from quantum Teichmuller theory. In particular, we notice a discrepancy between the Kashaev quantization and the Chekhov-Fock quantization. In this talk, no knowledge on the subject is assumed, as I will start from a brief introduction to quantum Teichmuller theory. A relation to Liouville conformal field theory will also be mentioned.
reference : arXiv:1211.4300