Non-extendablity of Shelukhin's quasimorphism and non-triviality of Reznikov's class

2025/03/12 by Morimichi Kawasaki, Mitsuaki Kimura, Kawasaki, Morimichi +7 · 1 citation
Mathematics · #Analytic and geometric function theory #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2503.09455

openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

Shelukhin constructed a quasimorphism on the universal covering of the group of Hamiltonian diffeomorphisms for a general closed symplectic manifold. In the present paper, we prove the non-extendability of that quasimorphism for certain symplectic manifolds, such as a blow-up of torus and the product of a surface of genus at least two and a closed symplectic manifold. As its application, we prove the non-vanishing of Reznikov's characteristic class for the above symplectic manifolds.

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