Braid group actions on branched coverings and full exceptional sequences

Wen Chang; Fabian Haiden; Sibylle Schroll

doi:10.48550/arXiv.2301.04398

Braid group actions on branched coverings and full exceptional sequences

Wen Chang, Fabian Haiden, Sibylle Schroll

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Abstract

We relate full exceptional sequences in Fukaya categories of surfaces or equivalently in derived categories of graded gentle algebras to branched coverings over the disk, building on a previous classification result of the first and third author. This allows us to apply tools from the theory of branched coverings such as Birman--Hilden theory and Hurwitz systems to study the natural braid group action on exceptional sequences. As an application, counterexamples are given to a conjecture of Bondal--Polishchuk on the transitivity of the braid group action on full exceptional sequences in a triangulated category.

Original language	English
Place of Publication	Cornell University
Publisher	arXiv.org
Number of pages	1
DOIs	https://doi.org/10.48550/arXiv.2301.04398
Publication status	Published - 11. Jan 2023

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Braid group actions on branched coverings and full exceptional sequences

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