SYMPLECTIC COHOMOLOGY AND A CONJECTURE OF VITERBO

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. This settles a well-known conjecture of Viterbo from 2007 as the special case of T-n, which has been completely open for n > 1. Our methods are different and more intrinsic than those of the previous work of the author first settling the case n = 1. The new 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. It contains spheres and is closed under products. We discuss generalizations and various applications, to C-0 symplectic topology in particular.