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.
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