Legendrian submanifolds from Bohr-Sommerfeld covers of monotone Lagrangian tori

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10494271" target="_blank" >RIV/00216208:11320/23:10494271 - isvavai.cz</a>

Výsledek na webu

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

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4310/CAG.2023.v31.n4.a6" target="_blank" >10.4310/CAG.2023.v31.n4.a6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Legendrian submanifolds from Bohr-Sommerfeld covers of monotone Lagrangian tori

Popis výsledku v původním jazyce

By a result due to Ziltener, there exist no closed embedded Bohr-Sommerfeld Lagrangians inside CP n for the prequantisation bun-dle whose total space is the standard contact sphere. On the otherhand, any embedded monotone Lagrangian torus has a canoni-cal nontrivial cover which is a Bohr-Sommerfeld immersion. Wedraw the front projections for the corresponding Legendrian liftsinside a contact Darboux ball of the threefold covers of both thetwo-dimensional Clifford and Chekanov tori (the former is the Leg-endrian link of the Harvey-Lawson special Lagrangian cone), andcompute the associated Chekanov-Eliashberg algebras. Althoughthese Legendrians are not loose, we show that they both admitexact Lagrangian cobordisms to the loose Legendrian sphere; theyhence admit exact Lagrangian caps in the symplectisation, whichare non-regular Lagrangian cobordisms. Along the way, we alsocompute bilinearised Legendrian contact homology of a generalLegendrian surface in the standard contact vector space when allReeb chords are of positive degree, as well as the augmentationvariety in the case of tori

Název v anglickém jazyce

Legendrian submanifolds from Bohr-Sommerfeld covers of monotone Lagrangian tori

Popis výsledku anglicky

By a result due to Ziltener, there exist no closed embedded Bohr-Sommerfeld Lagrangians inside CP n for the prequantisation bun-dle whose total space is the standard contact sphere. On the otherhand, any embedded monotone Lagrangian torus has a canoni-cal nontrivial cover which is a Bohr-Sommerfeld immersion. Wedraw the front projections for the corresponding Legendrian liftsinside a contact Darboux ball of the threefold covers of both thetwo-dimensional Clifford and Chekanov tori (the former is the Leg-endrian link of the Harvey-Lawson special Lagrangian cone), andcompute the associated Chekanov-Eliashberg algebras. Althoughthese Legendrians are not loose, we show that they both admitexact Lagrangian cobordisms to the loose Legendrian sphere; theyhence admit exact Lagrangian caps in the symplectisation, whichare non-regular Lagrangian cobordisms. Along the way, we alsocompute bilinearised Legendrian contact homology of a generalLegendrian surface in the standard contact vector space when allReeb chords are of positive degree, as well as the augmentationvariety in the case of tori

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

2023

Kód důvěrnosti údajů

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

Název periodika

Communications in Analysis and Geometry

ISSN

1019-8385

e-ISSN

1944-9992

Svazek periodika

31

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

HK - Hongkong

Počet stran výsledku

73

Strana od-do

905-977

Kód UT WoS článku

001434393600006

EID výsledku v databázi Scopus

2-s2.0-85199896478