Proper and Isometric Actions

Marcos M. Alexandrino and Renato G. Bettiol
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Marcos M. Alexandrino: Instituto de Matemática e Estatística Universidade de São Paulo, Departamento de Matemática
Renato G. Bettiol: University of Pennsylvania, Department of Mathematics

Chapter Chapter 3 in Lie Groups and Geometric Aspects of Isometric Actions, 2015, pp 51-84 from Springer

Abstract: Abstract In this chapter, we present a concise introduction to the theory of proper and isometric actions. We begin with basic definitions and a quick primer on fiber bundles, leading to the Slice Theorem 3.49 and the Tubular Neighborhood Theorem 3.57. These fundamental results are used throughout the rest of the book; in particular, to establish a strong correspondence between proper and isometric actions in Sect. 3.3. Finally, the stratification of a manifold by orbit types of a proper action is studied in Sect. 3.5.

Keywords: Isometric Action; Tubular Neighborhood Theorem; Type Orbitals; Proper Action; Quick Primer (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-16613-1_3

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DOI: 10.1007/978-3-319-16613-1_3

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