LAGRANGIAN CONCORDANCE IS NOT A PARTIAL ORDER IN HIGH DIMENSIONS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10508913" target="_blank" >RIV/00216208:11320/25:10508913 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wxMOuw.Q8m" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wxMOuw.Q8m</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2140/pjm.2025.334.183" target="_blank" >10.2140/pjm.2025.334.183</a>

Result language
angličtina
Original language name
LAGRANGIAN CONCORDANCE IS NOT A PARTIAL ORDER IN HIGH DIMENSIONS
Original language description
We provide examples of pairs of closed, connected Legendrian nonisotopic Legendrian submanifolds (Lambda(-), Lambda(+)) of the (4n+1)-dimensional contact vector space, n > 1, such that there exist Lagrangian concordances from Lambda(-) to Lambda(+) and from Lambda(+) to Lambda(-). This contradicts antisymmetry of the Lagrangian concordance relation, and, in particular, implies that Lagrangian concordances with connected Legendrian ends do not define a partial order in high dimensions. In addition, we explain how to get the same result for the relation given by exact Lagrangian cobordisms with connected Legendrian ends in the (2n+1)-dimensional contact vector space, n > 1.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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