Py-Calabi quasi-morphisms and quasi-states on orientable surfaces of higher genus (Q616517)

The author shows that a Py-Calabi quasi-morphism on an orientable surface \(M\) of higher genus determines a quasi-state. The proof is very technical. He defines a functional such that the extension to the commutative Banach algebra of all continuous functions on \(M\) is a quasi-state. Then, he shows its monotonicity and continuity. In order to prove its monotonicity, he uses the following results: he constructs a pair of pants decomposition using a generic Morse function and gives an intersection theorem of figure eights related to the pair of pants decomposition.