Symplectic cohomology and a conjecture of Viterbo

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 $T^n.$ 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.