Basic kirwan injectivity and its applications

Abstract Consider the Hamiltonian action of a torus on transversely symplectic foliation that is also Riemannian. When transverse hard Lefschetz property satisfied, we establish foliated version Kirwan injectivity theorem and use it to study actions Kähler foliations. Among other things, prove analogue Carrell–Liberman theorem. As an application, this confirms conjecture raised by Battaglia–Zaffran basic Hodge numbers toric quasifolds. Our methods allow us present approach calculation Betti