Covariantly functorial wrapped Floer theory on Liouville sectors

By Sheel Ganatra, J. Pardon, Vivek V. Shende. Publications mathématiques (Bures-sur-Yvette), 2017

185 citations recorded by the source corpus.

We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid’s generation criterion follows.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4146253f64ca263120c86aa43316af6bc6b036f4

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Citations in the corpus

Microlocal Morse theory of wrapped Fukaya categories (2018, methodology): “In fact it would not have helped to do so: beyond the foundations we set up in [19, 20], the main new ideas and difficulties in the proof of Theorem 1.”
Sectorial descent for wrapped Fukaya categories (2018, background): “ Fukaya categories Let us begin by xing our notation and terminology for partially wrapped Fukaya categories (see x2for a full treatment); our setup is rather more general than that considered before [7,8,42,32,26]. For a Liouville manifold Xand any closed subset f @ 1X, henceforth referred to as a ”
On partially wrapped Fukaya categories (2016, background): “C, a low-action, length-3 fundamental cycle can be obtained from a ne decomposition of Finto triangles and strips. More generally, it is likely that a careful analysis of the continuation elements in [19] would show that any Weinstein domain with nontrivial symplectic cohomology admitting arbitraril”
Bounds on spectral norms and barcodes (2018, background): “ the modules are homologically unital, it can be given, in homology, by the operator of multiplication by a suitable homology class. This class is called a continuation element in the literature (cf. [2, 4, 48, 66]). Finally, considering the chain level and ltrations, it turns out benecial to replac”