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The homological content of the Jones representations at q =-1
Aarhus Univ, Fac Sci, Ctr Quantum Geometry Moduli Spaces, DK-8000 Aarhus C, Denmark..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 25, no 11, 1650062Article in journal (Refereed) Published
Abstract [en]

We generalize a discovery of Kasahara and show that the Jones representations of braid groups, when evaluated at q = -1, are related to the action on homology of a branched double cover of the underlying punctured disk. As an application, we prove for a large family of pseudo-Anosov mapping classes a conjecture put forward by Andersen, Masbaum, and Ueno [Topological quantum field theory and the Nielsen-Thurston classification of M(0, 4), Math. Proc. Cambridge Philos. Soc. 141(3) (2006) 477-488] by extending their original argument for the sphere with four marked points to our more general case.

Place, publisher, year, edition, pages
2016. Vol. 25, no 11, 1650062
Keyword [en]
Jones representation, braid group, mapping class group, topological quantum field theory, temperly-lieb algebra, quantum representation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-308934DOI: 10.1142/S0218216516500620ISI: 000386571400003OAI: oai:DiVA.org:uu-308934DiVA: diva2:1051137
Funder
Danish National Research Foundation, DNRF95Swedish Research Council, 621-2011-3629
Available from: 2016-12-01 Created: 2016-12-01 Last updated: 2016-12-01Bibliographically approved

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Jørgensen, Søren Fuglede
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