Seminar

A few remarks on the Arnold's chord estimate

Symplectic geometry and topology

10 November 14:00 - 15:00

Roman Golovko - Alfred Renyi Institute of Mathematics

Given a chord-generic horizontally displaceable Legendrian submanifold L of the contactization of a Liouville manifold with the property that its Chekanov-Eliashberg algebra admits a finite-dimensional matrix representation, we prove that the number of Reeb chords on L is bounded from below by half of the Betti numbers of L. This bound is called the homological Arnold-type lower bound. Moreover, if L admits an exact Lagrangian filling, we prove that the number of Reeb chords on L is bounded from below by the stable Morse number of the filling. In general, this bound is stronger than the homological Arnold-type lower bound. This is a joint work with Georgios Dimitroglou Rizell.
Organizers
Tobias Ekholm,
Uppsala University
Yakov Eliashberg
Stanford University
Lenhard Ng
Duke University
Ivan Smith
University of Cambridge

Program
Contact

Tobias Ekholm

tobias.ekholm@math.uu.se

Other
information

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