Homogeneous quasimorphisms, \(C^0\)-topology and Lagrangian intersection (Q2159484)

A (real) homogeneous quasimorphism on a group \(G\) is a map from \(G\) to the set of real numbers satisfying certain conditions. For symplectic manifolds, homogeneous quasimorphisms on the group of Hamiltonian diffeomorphisms have been extensively studied by many people. In this paper, the author constructs an example of a non-trivial homogeneous quasimorphism on the group of Hamiltonian diffeomorphisms of the two and four dimensional quadric hypersurfaces which is continuous with respect to the \(C^0\)-metric and the Hofer metric, and hence answers an open question of \textit{M. Entov} et al. [Prog. Math. 296, 169--197 (2012; Zbl 1251.53047)]. The main technique the author applies is the quantum cohomology of these spaces with different coefficients.