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Cohomological invariants of twisted wild character varieties as constructed by Boalch and Yamakawa are derived from enumerative Calabi-Yau geometry and refined Chern-Simons invariants of torus knots. Generalizing the untwisted case, the present approach is based on a spectral correspondence for meromorphic Higgs bundles with fixed conjugacy classes at the marked points. This construction is carried out for twisted wild character varieties associated to (l, kl-1) torus knots, providing a colored generalization of existing results of Hausel, Mereb and Wong as well as Shende, Treumann and Zaslow.
The recently conjectured knots-quivers correspondence relates gauge theoretic invariants of a knot $K$ in the 3-sphere to representation theory of a quiver $Q_{K}$ associated to the knot. In this paper we provide geometric and physical contexts for t
We show that no torus knot of type $(2,n)$, $n>3$ odd, can be obtained from a polynomial embedding $t mapsto (f(t), g(t), h(t))$ where $(deg(f),deg(g))leq (3,n+1) $. Eventually, we give explicit examples with minimal lexicographic degree.
We present the formulation of the bosonic Hamiltonian M2-brane compactified on a twice punctured torus following the procedure proposed in cite{mpgm14}. In this work we analyse two possible metric choice, different from the one used in cite{mpgm14},
The 2d gauged linear sigma model (GLSM) gives a UV model for quantum cohomology on a Kahler manifold X, which is reproduced in the IR limit. We propose and explore a 3d lift of this correspondence, where the UV model is the N=2 supersymmetric 3d gaug
We generalize unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces of the form $Sigmatimes [0,1]$ for $Sigma$ a compact closed 2-manifold up to stable equivalence. We introduce a