IMAGES of QUANTUM REPRESENTATIONS of MAPPING CLASS GROUPS and DUPONT-GUICHARDET-WIGNER QUASI-HOMOMORPHISMS

Louis Funar, Wolfgang Pitsch

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2 Citations (Scopus)

Abstract

© Cambridge University Press 2016. We prove that either the images of the mapping class groups by quantum representations are not isomorphic to higher rank lattices or else the kernels have a large number of normal generators. Further, we show that the images of the mapping class groups have non-trivial 2-cohomology, at least for small levels. For this purpose, we considered a series of quasi-homomorphisms on mapping class groups extending the previous work of Barge and Ghys (Math. Ann. 294 (1992), 235-265) and of Gambaudo and Ghys (Bull. Soc. Math. France 133(4) (2005), 541-579). These quasi-homomorphisms are pull-backs of the Dupont-Guichardet-Wigner quasi-homomorphisms on pseudo-unitary groups along quantum representations.
Original languageEnglish
Pages (from-to)277-304
JournalJournal of the Institute of Mathematics of Jussieu
Volume17
Issue number2
DOIs
Publication statusPublished - 1 Apr 2018

Keywords

  • Dupont-Guichardet-Wigner cocycle
  • central extension
  • group homology
  • mapping class group
  • pseudo-unitary group
  • quantum representation
  • quasi-homomorphism
  • symplectic group

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