Sur les rétractions d’une variété. (On the retractions of a manifold). (French) Zbl 0609.32021

If \(f: X\to X\) is a function, then \(Fix(f)=\{x\in X: f(x)=x\}\); and f is called a retraction if \(f\circ f=f\). Here it is shown in great generality that if f is a retraction, then Fix(f) is a smooth manifold; and near \(x_ 0\in Fix(f)\) f may be represented by a linear retraction.
Reviewer: E.Bedford


32H99 Holomorphic mappings and correspondences
32Q99 Complex manifolds
57R45 Singularities of differentiable mappings in differential topology