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arXiv · 1407.3526

The Morse-Bott-Kirwan condition is local

Tara Holm·Yael Karshon
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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.

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Tara Holm, Yael Karshon. 2016-11-09. The Morse-Bott-Kirwan condition is local. https://doi.org/10.1186/s40687-016-0066-9

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