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arXiv · 1904.06798

Symplectic cohomology and a conjecture of Viterbo

Egor Shelukhin
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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.

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Egor Shelukhin. 2019-04-15. Symplectic cohomology and a conjecture of Viterbo. https://arxiv.org/abs/1904.06798

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