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arXiv · 1908.02317

Orlov and Viterbo functors in partially wrapped Fukaya categories

Zachary Sylvan
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Abstract

We study two functors between (partially) wrapped Fukaya categories. The first is the Orlov functor from the Fukaya category of a stop to the Fukaya category of the ambient sector. We give a geometric criterion for when this functor is spherical in the sense of Anno-Logvinenko. This criterion is a generalization of the situation where the stop comes from a Landau-Ginzburg model. The second functor is the Viterbo transfer map from a Liouville domain to a subdomain. We show that when the domain and subdomain are independently Weinstein, this functor is a homological epimorphism, which means that it becomes a localization after passing to module categories. This should be compared with a result of Ganatra-Pardon-Shende, which states that the Viterbo map is a genuine localization when the cobordism is Weinstein.

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Zachary Sylvan. 2019-08-06. Orlov and Viterbo functors in partially wrapped Fukaya categories. https://arxiv.org/abs/1908.02317

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