A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds. I

DOI10.1007/BF02102409zbMath0872.57010arXivhep-th/9401061OpenAlexW1993127353MaRDI QIDQ1912599

Lev Rozansky

Publication date: 8 October 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9401061

zbMATH Keywords

path integralAlexander polynomialJones polynomialrational homology spheresCasson-Walker invariantChern-Simons quantum field theoryWitten's invariant

Mathematics Subject Classification ID

Related Items (38)

Holomorphic blocks in three dimensions ⋮ The trivial connection contribution to Witten's invariant and finite type invariants of rational homology spheres ⋮ Quantum invariants, modular forms, and lattice points II ⋮ Chern-Simons theory and S-duality ⋮ Branches, quivers, and ideals for knot complements ⋮ ON OHTSUKI'S INVARIANTS OF HOMOLOGY 3-SPHERES ⋮ Remodeling the B-model ⋮ CHERN–SIMONS THEORY AND THE QUANTUM RACAH FORMULA ⋮ Higher order terms in the Melvin-Morton expansion of the colored Jones polynomial ⋮ Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant ⋮ Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants ⋮ ASYMPTOTIC BEHAVIORS OF THE COLORED JONES POLYNOMIALS OF A TORUS KNOT ⋮ ON THE QUANTUM INVARIANT FOR THE BRIESKORN HOMOLOGY SPHERES ⋮ A contribution of the trivial connection of the Jones polynomial and Witten's invariant of 3d manifolds. II ⋮ Ray-Singer torsion for a hyperbolic 3-manifold and asymptotics of Chern-Simons-Witten invariant ⋮ Revisiting the Melvin-Morton-Rozansky expansion, or there and back again ⋮ BPS invariants for Seifert manifolds ⋮ RESHETIKHIN–TURAEV INVARIANTS OF SEIFERT 3-MANIFOLDS FOR CLASSICAL SIMPLE LIE ALGEBRAS ⋮ On \(p\)-adic convergence of perturbative invariants of some rational homology spheres ⋮ Torus knots in lens spaces and topological strings ⋮ Chern-Simons models on \(S^2\times S^1\), torus gauge fixing, and link invariants II ⋮ Quivers for 3-manifolds: the correspondence, BPS states, and 3d \(\mathcal{N} = 2\) theories ⋮ DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT ⋮ Nonperturbative black hole entropy and Kloosterman sums ⋮ Semiclassical approximation for Chern-Simons theory and \(3\)-hyperbolic invariants. ⋮ The colored Jones polynomials and the simplicial volume of a knot ⋮ Large N duality beyond the genus expansion ⋮ On the quantum invariants for the spherical Seifert manifolds ⋮ On knots, complements, and \(6j\)-symbols ⋮ A two-variable series for knot complements ⋮ Knots and graphs ⋮ AN L²-ALEXANDER INVARIANT FOR KNOTS ⋮ CHERN–SIMONS THEORY, EXACTLY SOLVABLE MODELS AND FREE FERMIONS AT FINITE TEMPERATURE ⋮ Three-manifold topology and the Donaldson-Witten partition function ⋮ ON HABIRO'S CYCLOTOMIC EXPANSIONS OF THE OHTSUKI INVARIANT ⋮ From simplicial Chern-Simons theory to the shadow invariant I ⋮ Three-dimensional quantum gravity, Chern-Simons theory, and the \(A\)-polynomial ⋮ \({\widehat{Z}}\) at large \(N\): from curve counts to quantum modularity

Cites Work

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• The coloured Jones function
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• R-torsion and the Laplacian on Riemannian manifolds
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