scholarly journals Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation

1992 ◽  
Vol 147 (3) ◽  
pp. 563-604 ◽  
Author(s):  
Lisa C. Jeffrey
Keyword(s):  
Semiclassical Approximation ◽  
Lens Spaces ◽  
Torus Bundles ◽  
Chern Simons

scholarly journals On the Witten–Reshetikhin–Turaev invariants of torus bundles

2015 ◽  
Vol 24 (11) ◽  
pp. 1550055
Author(s):  
Jørgen Ellegaard Andersen ◽  
Søren Fuglede Jørgensen
Keyword(s):  
Growth Rate ◽  
Asymptotic Expansion ◽  
Semiclassical Approximation ◽  
Lens Spaces ◽  
Commun Math Phys ◽  
Torus Bundles ◽  
Mapping Tori ◽  
Chern Simons ◽  
Math Phys

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.

scholarly journals Topological strings, two-dimensional Yang-Mills theory and Chern-Simons theory on torus bundles

2008 ◽  
Vol 12 (5) ◽  
pp. 981-1058 ◽  
Author(s):  
Nicola Caporaso ◽  
Michele Cirafici ◽  
Luca Griguolo ◽  
Sara Pasquetti ◽  
Domenico Seminara ◽  
...  
Keyword(s):  
Topological Strings ◽  
Simons Theory ◽  
Two Dimensional ◽  
Yang Mills ◽  
Torus Bundles ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals Chern–Simons theory on L(p,q) lens spaces and Gopakumar–Vafa duality

2010 ◽  
Vol 60 (3) ◽  
pp. 417-429 ◽  
Author(s):  
Andrea Brini ◽  
Luca Griguolo ◽  
Domenico Seminara ◽  
Alessandro Tanzini
Keyword(s):  
Lens Spaces ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals TORSION ON HYPERBOLIC MANIFOLDS AND THE SEMICLASSICAL LIMIT FOR CHERN–SIMONS THEORY

1998 ◽  
Vol 13 (30) ◽  
pp. 2453-2461 ◽  
Author(s):  
A. A. BYTSENKO ◽  
A. E. GONÇALVES ◽  
W. DA CRUZ
Keyword(s):  
Integration Method ◽  
Semiclassical Approximation ◽  
Semiclassical Limit ◽  
Hyperbolic Manifolds ◽  
Simons Theory ◽  
Manifold With Boundary ◽  
Hyperbolic Three Manifolds ◽  
Chern Simons ◽  
Chern Simons Theory ◽  
Invariant Integration

The invariant integration method for Chern–Simons theory of gauge group SU(2) and manifold Γ\H3 is verified in the semiclassical limit. The semiclassical approximation for the partition function associated with a connected sum of hyperbolic three-manifolds is presented. We discuss briefly L2-analytical and topological torsions of a manifold with boundary.

The Absolute Value of The Chern-Simons-Witten Invariants of Lens Spaces

1995 ◽  
Vol 04 (02) ◽  
pp. 319-327 ◽  
Author(s):  
SHUJI YAMADA
Keyword(s):  
Explicit Formula ◽  
Lens Spaces ◽  
Homotopy Equivalence ◽  
Absolute Value ◽  
The Absolute ◽  
Chern Simons

An explicit formula for the absolute value of the Witten invariants is derived. We discuss the relation between homotopy equivalence and the absolute value of Witten invariants for lens spaces. We also give examples of arbitrarily finitely many lens spaces which have the same Witten invariants for any level r.

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