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Matrix factorizations and link homology
Author(s): Khovanov, Mikhail; Rozansky, Lev | Abstract: For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the
Hyper-Kähler geometry and invariants of three-manifolds
Abstract We study a 3-dimensional topological sigma-model, whose target space is a hyper-Kähler manifold X. A Feynman diagram calculation of its partition function demonstrates that it is a finite
Witten–Reshetikhin–Turaev Invariants of¶Seifert Manifolds
Abstract:For Seifert homology spheres, we derive a holomorphic function of K whose value at integer K is the sl2 Witten–Reshetikhin–Turaev invariant, ZK, at q= exp 2πi/K. This function is expressed
Matrix factorizations and link homology II
For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a
The Århus integral of rational homology 3-spheres II: Invariance and universality
Abstract. We continue the work started in [Å-I], and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Århus integral
Quantum field theory for the multi-variable Alexander-Conway polynomial
Abstract We investigate in this paper the quantum field theory description of the multi-variable Alexander polynomial (Δ). We first study the WZW model on the GL(1, 1). It presents a number of
Topological Landau-Ginzburg models on the world-sheet foam
We define topological Landau-Ginzburg models on a world-sheet foam, that is, on a collection of 2-dimensional surfaces whose boundaries are sewn together along the edges of a graph. We use matrix
A largek asymptotics of Witten's invariant of Seifert manifolds
We calculate a largek asymptotic expansion of the exact surgery formula for Witten'sSU(2) invariant of some Seifert manifolds. The contributions of all flat connections are identified. An agreement
The Aarhus integral of rational homology 3-spheres I: A highly non trivial flat connection on S^3
Path integrals don't really exist, but it is very useful to dream that they do exist, and figure out the consequences. Apart from describing much of the physical world as we now know it, these dreams
A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds, I
We use a path integral formulation of the Chern-Simons quantum field theory in order to give a simple “semi-rigorous” proof of a recently conjectured limitation on the 1/K expansion of the Jones
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