L^2-cohomology and complete Hamiltonian manifolds

Thursday, 15 January, 2015

Published in: 

Journal of Geometry and Physics, Volume 87, January 2015, Pages 305–313

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.

Author(s): 

Rafe Mazzeo
Álvaro Pelayo
Tudor S. Ratiu