L^2-Cohomology and complete Hamiltonian manifolds
Symplectic Geometry
2015-06-18 v1 Differential Geometry
Functional Analysis
Abstract
A classical theorem of Frankel for compact K\"ahler manifolds states that a K\"ahler S^1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when Hodge theory holds on non-compact manifolds, then Frankel's theorem still holds. Finally, we present several concrete situations in which the assumptions of the metatheorem hold.
Keywords
Cite
@article{arxiv.1402.0098,
title = {L^2-Cohomology and complete Hamiltonian manifolds},
author = {Rafe Mazzeo and Álvaro Pelayo and Tudor Ratiu},
journal= {arXiv preprint arXiv:1402.0098},
year = {2015}
}
Comments
14 pages. This article expands and improves on arxiv:1005.2163