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Skeins and mapping class groups

Published online by Cambridge University Press:  24 October 2008

Justin Roberts
Justin Roberts
Affiliation:
D.P.M.M.S., 16 Mill Lane, Cambridge CB2 1SB
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Abstract

The protective unitary representations of the mapping class groups of surfaces corresponding to the Jones–Witten topological quantum field theory for SU(2) are expressed as representations in algebras of skeins in the surface. The skein-theoretic construction of the representations uses neither Kirby's surgery theorem nor a presentation of the group. Using these representations and the Reidemeister–Singer classification of Heegaard splittings gives a proof of the existence of the moduli of the Witten invariants of 3-manifolds.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 1 , January 1994 , pp. 53 - 77
Copyright
Copyright © Cambridge Philosophical Society 1994

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