Quantitative Heegaard Floer cohomology and the Calabi invariant

Abstract We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces any genus. show that our recover the Calabi invariant Hamiltonians their limit. As applications, we resolve several open questions from topological surface dynamics continuous symplectic topology: group Hamiltonian homeomorphisms with (possibly empty) boundary is not simple; extend homomorphism hameomorphisms constructed by Oh Müller, construct an infinite-dimensional quasi-morphisms on area orientation preserving two-sphere. Our are inspired recent work Polterovich Shelukhin defining applying invariants, via orbifold Floer homology, for composed parallel circles A particular feature it avoids setting relies instead ‘classical’ homology. This only substantially simplifies technical background but seems essential some aspects (such as application constructing quasi-morphisms).