A filtered A-infinity category, the Legendrian CI Fukaya category, is defined using moduli spaces of contact instantons with Reeb chord asymptotics.
Calabi-Yau structures on Rabinowitz Fukaya categories
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abstract
In this paper, we prove that the derived Rabinowitz Fukaya category of a Liouville domain $M$ of dimension $2n$ is $(n-1)$-Calabi--Yau assuming the wrapped Fukaya category of $M$ admits an at most countable set of Lagrangians that generate it and satisfy some finiteness condition on morphism spaces between them.
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2024 1verdicts
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Rational contact instantons and Legendrian Fukaya category
A filtered A-infinity category, the Legendrian CI Fukaya category, is defined using moduli spaces of contact instantons with Reeb chord asymptotics.