Symplectic cohomology and a conjecture of Viterbo

2019/04/15 by Shelukhin, Egor · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1904.06798

Abstract

We identify a new class of closed smooth manifolds for which there exists a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in a unit cotangent disk bundle, settling a well-known conjecture of Viterbo from 2007 as the special case of Tⁿ. This class of manifolds is defined in topological terms involving the Chas-Sullivan algebra and the BV-operator on the homology of the free loop space, contains spheres and is closed under products. We discuss generalizations and various applications.

Cited by

• C⁰-rigidity of the Hamiltonian diffeomorphism group of symplectic rational surfaces

Related

• Viterbo conjecture for Zoll symmetric spaces
• Symplectic cohomology and Viterbo's theorem
• Families of Legendrians and Lagrangians with unbounded spectral norm
• Viterbo's spectral bound conjecture for homogeneous spaces
• Cohomological properties of ruled symplectic structures