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arXiv · 1409.8611

Flat surfaces and stability structures

Fabian Haiden·Ludmil Katzarkov·Maxim Kontsevich
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Abstract

We identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured surfaces. This is achieved by new methods involving the complete classification of objects in these categories, which are defined in an elementary way. We also introduce a number of tools to deal with surfaces of infinite area, where structures similar to those in cluster algebra appear.

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Fabian Haiden, Ludmil Katzarkov, Maxim Kontsevich. 2014-09-30. Flat surfaces and stability structures. https://doi.org/10.1007/s10240-017-0095-y

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