The stable Morse number as a lower bound for the number of Reeb chords

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10407802" target="_blank" >RIV/00216208:11320/19:10407802 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=h0sYhMgsEk" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=h0sYhMgsEk</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4310/JSG.2018.v16.n5.a2" target="_blank" >10.4310/JSG.2018.v16.n5.a2</a>

Result language
angličtina
Original language name
The stable Morse number as a lower bound for the number of Reeb chords
Original language description
Assume that we are given a closed chord-generic Legendrian sub-manifold Lambda subset of P x R of the contactisation of a Liouville manifold, where Lambda moreover admits an exact Lagrangian filling L-Lambda subset of R x P x R inside the symplectisation. Under the further assumptions that this filling is spin and has vanishing Maslov class, we prove that the number of Reeb chords on Lambda is bounded from below by the stable Morse number of L-Lambda. Given a general exact Lagrangian filling L-Lambda, we show that the number of Reeb chords is bounded from below by a quantity depending on the homotopy type of L-Lambda, following Ono-Pajitnov's implementation in Floer homology of invariants due to Sharko. This improves previously known bounds in terms of the Betti numbers of either Lambda or L-Lambda.
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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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