Twisted spectral correspondence and torus knots

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

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Twisted spectral correspondence and torus knots

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arxiv 1804.08364 v1 pith:RKNKLC6R submitted 2018-04-23 hep-th math.AG

Twisted spectral correspondence and torus knots

Wu-yen Chuang , Duiliu-Emanuel Diaconescu , Ron Donagi , Satoshi Nawata , Tony Pantev This is my paper

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keywords knotstorustwistedcharactercorrespondenceinvariantsspectralvarieties

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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.

Twisted spectral correspondence and torus knots

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