Twisted spectral correspondence and torus knots

Chuang, Wu-yen; Diaconescu, Duiliu-Emanuel; Donagi, Ron; Nawata, Satoshi; Pantev, Tony

doi:10.1142/S0218216520500406

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Twisted spectral correspondence and torus knots

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Nawata, Satoshi
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1142/S0218216520500406
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arXiv:1804.08364.pdf
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Citation

Chuang, W.-y., Diaconescu, D.-E., Donagi, R., Nawata, S., & Pantev, T. (2020). Twisted spectral correspondence and torus knots. Journal of Knot Theory and Its Ramifications, 29 (6): 2050040. doi:10.1142/S0218216520500406.

Cite as: https://hdl.handle.net/21.11116/0000-0006-982F-B

Abstract

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.