On C⁰-continuity of the spectral norm for symplectically non-aspherical manifolds

2019/05/19 by Yusuke Kawamoto, Kawamoto, Yusuke · 3 citations
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1905.07809

openalex publication_date 2019/05/19 · openalex created_date 2020/08/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to study the relation between the C⁰-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 C⁰-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 C⁰-continuity of the spectral norm proven by Shelukhin. We also prove a partial C⁰-continuity of the spectral norm for rational symplectic manifolds. Some applications such as the Arnold conjecture in the context of C⁰-symplectic topology are also discussed.

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• On the spectral diameter of the Grassmannians
• Lagrangian intersections and a conjecture of Arnol'd
• Hamiltonian no-torsion

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