GEOMETRIC GENERATION OF THE WRAPPED FUKAYA CATEGORY OF WEINSTEIN MANIFOLDS AND SECTORS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10494134" target="_blank" >RIV/00216208:11320/24:10494134 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cQ-xC5wEbx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cQ-xC5wEbx</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.24033/asens.2570" target="_blank" >10.24033/asens.2570</a>

Jazyk výsledku

angličtina

Název v původním jazyce

GEOMETRIC GENERATION OF THE WRAPPED FUKAYA CATEGORY OF WEINSTEIN MANIFOLDS AND SECTORS

Popis výsledku v původním jazyce

We prove that the wrapped Fukaya category of any 2n-dimensional Weinstein manifold (or, more generally, Weinstein sector) W is generated by the unstable manifolds of the index n critical points of its Liouville vector field. Our proof is geometric in nature, relying on a surgery formula for Floer cohomology and the fairly simple observation that Floer cohomology vanishes for Lagrangian submanifolds that can be disjoined from the isotropic skeleton of theWeinstein manifold. Note that we do not need any additional assumptions on this skeleton. By applying our generation result to the diagonal in the product W x W, we obtain as a corollary that the open-closed map from the Hochschild homology of the wrapped Fukaya category of W to its symplectic cohomology is an isomorphism, proving a conjecture of Seidel. We work mainly in the &quot;linear setup&quot; for the wrapped Fukaya category, but we also extend the proofs to the &quot;quadratic&quot; and &quot;localisation&quot; setup. This is necessary for dealing with Weinstein sectors and for the applications.

Název v anglickém jazyce

GEOMETRIC GENERATION OF THE WRAPPED FUKAYA CATEGORY OF WEINSTEIN MANIFOLDS AND SECTORS

Popis výsledku anglicky

We prove that the wrapped Fukaya category of any 2n-dimensional Weinstein manifold (or, more generally, Weinstein sector) W is generated by the unstable manifolds of the index n critical points of its Liouville vector field. Our proof is geometric in nature, relying on a surgery formula for Floer cohomology and the fairly simple observation that Floer cohomology vanishes for Lagrangian submanifolds that can be disjoined from the isotropic skeleton of theWeinstein manifold. Note that we do not need any additional assumptions on this skeleton. By applying our generation result to the diagonal in the product W x W, we obtain as a corollary that the open-closed map from the Hochschild homology of the wrapped Fukaya category of W to its symplectic cohomology is an isomorphism, proving a conjecture of Seidel. We work mainly in the &quot;linear setup&quot; for the wrapped Fukaya category, but we also extend the proofs to the &quot;quadratic&quot; and &quot;localisation&quot; setup. This is necessary for dealing with Weinstein sectors and for the applications.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annales Scientifiques de l&apos;École Normale Supérieure

ISSN

0012-9593

e-ISSN

1873-2151

Svazek periodika

57

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

85

Strana od-do

1-85

Kód UT WoS článku

001380705300002

EID výsledku v databázi Scopus

2-s2.0-85189902633