O Teorema de Slice

Abstract

Our goal in this work is to study the classic and celebrated Slice Theorem. Initially proven by Koszul, the Slice Theorem states that given a proper action of a Lie group on a manifold, there exists a slice passing through each point in M, i.e., a submanifold transversal to the orbit passing through the given point with some special properties. This theorem is a fundamental tool in the Theory of Transformation Groups. This result allows us to reduce the study of a Lie group action near an orbit to the study of the geometry transversal to the orbit.