The Morse-Bott-Kirwan condition is local
Symplectic Geometry
2016-11-10 v2
Abstract
Kirwan identified a condition on a smooth function under which the usual techniques of Morse-Bott theory can be applied to this function. We prove that if a function satisfies this condition locally then it also satisfies the condition globally. As an application, we use the local normal form theorem to recover Kirwan's result that the norm-square of a momentum map satisfies Kirwan's condition.
Cite
@article{arxiv.1407.3526,
title = {The Morse-Bott-Kirwan condition is local},
author = {Tara Holm and Yael Karshon},
journal= {arXiv preprint arXiv:1407.3526},
year = {2016}
}
Comments
25 pages, one figure. v2: corrected some proofs