Symplectic cohomology and a conjecture of Viterbo - Shelukhin, Egor (Geometric and functional analysis, 2022)
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.