The Morse-Bott-Kirwan condition is local
arXiv:1407.3526 · doi:10.1186/s40687-016-0066-9
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.
25 pages, one figure. v2: corrected some proofs