L^2-cohomology and complete Hamiltonian manifolds

Rafe Mazzeo (1) , Álvaro Pelayo (2) , Tudor S. Ratiu (3)

1 Department of Mathematics
2 MATH - UC San Diego - Department of Mathematics [Univ California San Diego]
3 EPFL - Ecole Polytechnique Fédérale de Lausanne

A classical theorem of Frankel for compact Kähler manifolds states that a Kähler S^1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem still holds. Finally, we present several concrete situations in which the assumptions of the metatheorem hold.

Domaines: Physique mathématique [math-ph]

Rafe Mazzeo, Álvaro Pelayo, Tudor S. Ratiu. L^2-cohomology and complete Hamiltonian manifolds. Journal of Geometry and Physics, 2015, 87, pp.305-313. ⟨hal-01397877⟩