Mathematical Institute of the Serbian Academy of Sciences and Arts
|Title:||Branches, quivers, and ideals for knot complements||Journal:||Journal of Geometry and Physics||Volume:||177||First page:||104520||Issue Date:||1-Jul-2022||Rank:||~M22||ISSN:||0393-0440||DOI:||10.1016/j.geomphys.2022.104520||Abstract:||
We generalize the FK invariant, i.e. Zˆ for the complement of a knot K in the 3-sphere, the knots-quivers correspondence, and A-polynomials of knots, and find several interconnections between them. We associate an FK invariant to any branch of the A-polynomial of K and we work out explicit expressions for several simple knots. We show that these FK invariants can be written in the form of a quiver generating series, in analogy with the knots-quivers correspondence. We discuss various methods to obtain such quiver representations, among others using R-matrices. We generalize the quantum a-deformed A-polynomial to an ideal that contains the recursion relation in the group rank, i.e. in the parameter a, and describe its classical limit in terms of the Coulomb branch of a 3d-5d theory. We also provide t-deformed versions. Furthermore, we study how the quiver formulation for closed 3-manifolds obtained by surgery leads to the superpotential of 3d N=2 theory T[M3] and to the data of the associated modular tensor category MTC[M3].
|Keywords:||A polynomial | Open curve counts | Quantum invariants; High Energy Physics - Theory; High Energy Physics - Theory; Mathematics - Geometric Topology; Mathematics - Quantum Algebra; Mathematics - Symplectic Geometry||Publisher:||Elsevier|
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