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The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization

Title
The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization
Authors
Kim, Hyun Kyu
Ewha Authors
김현규
Issue Date
2016
Journal Title
ADVANCES IN MATHEMATICS
ISSN
0001-8708JCR Link

1090-2082JCR Link
Citation
ADVANCES IN MATHEMATICS vol. 293, pp. 529 - 588
Keywords
Quantum Teichmuller theoryThompson group TPtolemy-Thompson groupKashaev quantizationBraided Ptolemy-Thompson groupUniversal Teichmuller spaceStable braid groupInfinite braid group
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Indexed
SCI; SCIE; SCOPUS WOS
Document Type
Article
Abstract
Quantization of universal Teichmuller space provides projective representations of the Ptolemy-Thompson group, which is isomorphic to the Thompson group T. This yields certain central extensions of T by Z, called dilogarithmic central extensions. We compute a presentation of the dilogarithmic central extension (T) over cap (Kash) of T resulting from the Kashaev quantization, and show that it corresponds to 6 times the Euler class in H-2 (T; Z). Meanwhile, the braided Ptolemy-Thompson groups T*, T-# of Funar-Kapoudjian are extensions of T by the infinite braid group B-infinity and by abelianizing the kernel B-infinity one constructs central extensions T-ab*, T-ab(#) of T by Z, which are of topological nature. We show (T) over cap (Kash) congruent to T-ab(#) Our result is analogous to that of Funar and Sergiescu, who computed a presentation of another dilogarithmic central extension (T) over cap (CF) of T resulting from the Chekhov-Fock (-Goncharov) quantization and thus showed that it corresponds to 12 times the Euler class and that (T) over cap (CF) congruent to T-ab*. In addition, we suggest a natural relationship between the two quantizations in the level of projective representations. (C) 2016 Elsevier Inc. All rights reserved.
DOI
10.1016/j.aim.2016.02.016
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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