On $C^0$-continuity of the spectral norm for symplectically non-aspherical manifolds

Abstract

The purpose of this paper is to study the relation between the $C^0$-topology and the topology induced by the spectral norm on the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. Following the approach of Buhovsky-Humilière-Seyfaddini, we prove the $C^0$-continuity of the spectral norm for complex projective spaces and negative monotone symplectic manifolds. The case of complex projective spaces provides an alternative approach to the $C^0$-continuity of the spectral norm proven by Shelukhin. We also prove a partial $C^0$-continuity of the spectral norm for rational symplectic manifolds. Some applications such as the Arnold conjecture in the context of $C^0$-symplectic topology are also discussed.

v3. new title, no change in results, exposition largely revised. v4. accepted version, to appear in Int. Math. Res. Not. IMRN

References in corpus (2)

• Bounds on spectral norms and barcodes
• The action spectrum and C^0 symplectic topology

Cited by in corpus (4)

• The action spectrum and C^0 symplectic topology
• Hamiltonian no-torsion
• Dehn-Seidel twist, $C^0$ symplectic topology and barcodes
• Lagrangian intersections and a conjecture of Arnol'd