The homological content of the Jones representations at q =-1
2016 (English)In: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 25, no 11, 1650062Article in journal (Refereed) Published
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
Jones representation, braid group, mapping class group, topological quantum field theory, temperly-lieb algebra, quantum representation
IdentifiersURN: urn:nbn:se:uu:diva-308934DOI: 10.1142/S0218216516500620ISI: 000386571400003OAI: oai:DiVA.org:uu-308934DiVA: diva2:1051137
FunderDanish National Research Foundation, DNRF95Swedish Research Council, 621-2011-3629