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

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

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 GB
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

Keywords

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

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)
Computational Mathematics
Applied Mathematics

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10.1186/s40687-016-0066-9

Cite this

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title = "The Morse{\textendash}Bott{\textendash}Kirwan condition is local",

abstract = "Kirwan identified a condition on a smooth function under which the usual techniques of Morse{\textendash}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.",

keywords = "Hamiltonian group action, Kirwan surjectivity, Momentum map, Morse theory, Morse{\textendash}Bott",

author = "Tara Holm and Yael Karshon",

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doi = "10.1186/s40687-016-0066-9",

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AU - Holm, Tara

AU - Karshon, Yael

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - Hamiltonian group action

KW - Kirwan surjectivity

KW - Momentum map

KW - Morse theory

KW - Morse–Bott

UR - https://www.scopus.com/pages/publications/85050391583

U2 - 10.1186/s40687-016-0066-9

DO - 10.1186/s40687-016-0066-9

M3 - مقالة

SN - 2522-0144

VL - 3

JO - Research in Mathematical Sciences

JF - Research in Mathematical Sciences

IS - 1

M1 - 25

ER -

The Morse–Bott–Kirwan condition is local

Abstract

Keywords

ASJC Scopus subject areas

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