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arXiv · 2503.20906

Speculations on higher Fukaya categories

James Pascaleff·Nicolò Sibilla
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Abstract

We investigate a possible theory of higher Fukaya categories associated to $n$-shifted symplectic stacks, where $n \geq 0$. We consider two paradigmatic cases, the shifted cotangent stack of a smooth manifold and the coadjoint stack of a compact Lie group, drawing connections to the work of Teleman and 3D mirror symmetry. Our evidence includes some new results in $1$-shifted symplectic geometry.

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James Pascaleff, Nicolò Sibilla. 2025-03-26. Speculations on higher Fukaya categories. https://arxiv.org/abs/2503.20906

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