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Date | Mar 18, 2014 |
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Speaker | 김현규 |

Dept. | KIAS |

Room | 129-307 |

Time | 16:00-17:00 |

Quantization of the Teichmuller space of a surface yields projective representations of the mapping class group and hence central extensions of it. Universal case yields a central extension of the Thompson group T, which is the mapping class group of the unit disc with certain boundary condition. On the other hand, the mapping class group of the surface obtained by introducing infinite number of punctures inside the unit disc is an extension of T by infinite braid group. By abelianizing the infinite braid group, one obtains a central extension of T, which is shown to be isomorphic to the one coming from quantum Teichmuller theory. Two different ways of introducing punctures lead to two different central extensions, corresponding respectively to Kashaev quantization and Chekhov-Fock-Goncharov quantization. (Arxiv:1211.4300)

The talk will be made as elementary as possible, and no prior exposure to the theory of quantization is necessary.

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