The Morse–Bott–Kirwan condition is local

Tara Holm; Yael Karshon

doi:10.1186/s40687-016-0066-9

The Morse–Bott–Kirwan condition is local

Tara Holm^*, Yael Karshon

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Article number	25
Journal	Research in Mathematical Sciences
Volume	3
Issue number	1
DOIs	https://doi.org/10.1186/s40687-016-0066-9
State	Published - 1 Dec 2016
Externally published	Yes

Funding

Funders	Funder number
National Science Foundation	DMS-1206466
Directorate for Mathematical and Physical Sciences	1206466
Simons Foundation	208975
Natural Sciences and Engineering Research Council of Canada
Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada

Keywords

Hamiltonian group action
Kirwan surjectivity
Momentum map
Morse theory
Morse–Bott

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10.1186/s40687-016-0066-9

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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{\textquoteright}s result that the norm square of a momentum map satisfies Kirwan{\textquoteright}s condition.",

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The Morse–Bott–Kirwan condition is local

Abstract

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Keywords

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