Maslov class rigidity for Lagrangian submanifolds via Hofer's geometry

Kerman E., Sirikci N. İ.

COMMENTARII MATHEMATICI HELVETICI, vol.85, no.4, pp.907-949, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 85 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.4171/cmh/214
  • Journal Name: COMMENTARII MATHEMATICI HELVETICI
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.907-949
  • Keywords: Lagrangian submanifold, Maslov class, Floer theory, Hofer's geometry, SYMPLECTIC-MANIFOLDS, HAMILTONIAN-DYNAMICS, HOLOMORPHIC-CURVES, COTANGENT BUNDLES, FLOER HOMOLOGY, ENERGY, INDEX, TRANSVERSALITY, INTERSECTIONS, GEODESICS
  • Middle East Technical University Affiliated: No

Abstract

In this work, we establish new rigidity results for the Maslov class of Lagrangian submanifolds in large classes of closed and convex symplectic manifolds. Our main result establishes upper bounds for the minimal Maslov number of displaceable Lagrangian submanifolds which are product manifolds whose factors each admit a metric of negative sectional curvature. Such Lagrangian submanifolds exist in every symplectic manifold of dimension greater than six or equal to four.