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On the Witten–Reshetikhin–Turaev invariants of torus bundles
Centre for Quantum Geometry of Moduli Spaces, Aarhus University.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 24, no 11, 1550055Article in journal (Refereed) Published
Abstract [en]

By methods similar to those used by L. Jeffrey [L. C. Jeffrey, Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation, Commun. Math. Phys. 147 (1992) 563-604], we compute the quantum SU(N)-invariants for mapping tori of trace 2 homeomorphisms of a genus 1 surface when N = 2, 3 and discuss their asymptotics. In particular, we obtain directly a proof of a version of Witten's asymptotic expansion conjecture for these 3-manifolds. We further prove the growth rate conjecture for these 3-manifolds in the SU(2) case, where we also allow the 3-manifolds to contain certain knots. In this case we also discuss trace -2 homeomorphisms, obtaining - in combination with Jeffrey's results - a proof of the asymptotic expansion conjecture for all torus bundles.

Place, publisher, year, edition, pages
2015. Vol. 24, no 11, 1550055
Keyword [en]
Quantum invariants; TQFT; asymptotic expansion conjecture; Chern-Simons theory; moduli space of flat connections
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Research subject
URN: urn:nbn:se:uu:diva-265059DOI: 10.1142/S0218216515500558ISI: 000363426000003OAI: oai:DiVA.org:uu-265059DiVA: diva2:862354
Danish National Research Foundation
Available from: 2015-10-21 Created: 2015-10-21 Last updated: 2016-02-17Bibliographically approved

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Jørgensen, Søren Fuglede
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