dc.contributor.author Smith, Ivan dc.date.accessioned 2021-10-21T23:30:32Z dc.date.available 2021-10-21T23:30:32Z dc.date.issued 2021 dc.identifier.issn 0010-3616 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/329736 dc.description.abstract AbstractWe study threefolds Y fibred by $$A_m$$ A m -surfaces over a curve S of positive genus. An ideal triangulation of S defines, for each rank m, a quiver $$Q(\Delta _m)$$ Q ( Δ m ) , hence a $$CY_3$$ C Y 3 -category $$\mathcal {C}(W)$$ C ( W ) for any potential W on $$Q(\Delta _m)$$ Q ( Δ m ) . We show that for $$\omega$$ ω in an open subset of the Kähler cone, a subcategory of a sign-twisted Fukaya category of $$(Y,\omega )$$ ( Y , ω ) is quasi-isomorphic to $$(\mathcal {C},W_{[\omega ]})$$ ( C , W [ ω ] ) for a certain generic potential $$W_{[\omega ]}$$ W [ ω ] . This partially establishes a conjecture of Goncharov (in: Algebra, geometry, and physics in the 21st century, Birkhäuser/Springer, Cham, 2017) concerning ‘categorifications’ of cluster varieties of framed $${\mathbb {P}}GL_{m+1}$$ P G L m + 1 -local systems on S, and gives a symplectic geometric viewpoint on results of Gaiotto et al. (Ann Henri Poincaré 15(1):61–141, 2014) on ‘theories of class $${\mathcal {S}}$$ S ’. dc.publisher Springer Science and Business Media LLC dc.rights All rights reserved dc.rights.uri http://www.rioxx.net/licenses/all-rights-reserved dc.title Floer Theory of Higher Rank Quiver 3-folds dc.type Article prism.publicationName COMMUNICATIONS IN MATHEMATICAL PHYSICS dc.identifier.doi 10.17863/CAM.77183 dcterms.dateAccepted 2021-10-17 rioxxterms.versionofrecord 10.1007/s00220-021-04252-2 rioxxterms.version AM rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved rioxxterms.licenseref.startdate 2021-10-17 dc.identifier.eissn 1432-0916 rioxxterms.type Journal Article/Review pubs.funder-project-id Engineering and Physical Sciences Research Council (EP/N01815X/1) cam.issuedOnline 2021-11-11 cam.orpheus.success Tue Feb 01 19:02:05 GMT 2022 - Embargo updated cam.orpheus.counter 5 rioxxterms.freetoread.startdate 2022-11-11
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