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On the topology of isolated singularities in analytic spaces: José Seade
These notes have been prepared for my lectures at the CIMPA / UNESCO School on Dynamical Systems, to be held in Lima, Peru, this november of 2006. The aim is to give an introduction to some aspects of singularity theory. These are divided into five sections, corresponding to five my lectures. The first three sections discuss well-known material which is fundamental in the theory; the local conical structure of analytic sets, their relations with knots and links, resolution of surface singularities, Waldhausen manifolds, Milnor's fibration theorem for holomorphic functions and a beautiful theorem of Klein about surface singularities and finite subgroups of SU (2).
In the fourth section we give a refinement of Milnor's fibration theorem, which provides new insights into the geometry and topology of holomorphic functions near their critical points. In the last section we discuss Milnor fibrations for real analytic singularities.
Contents: 1. The local conical structure of analytic sets, 2. On complex surface singularities, 3. On Milnor's fibration theorem, 4. A refinement of Milnor's classical theorem, 5. Milnor fibrations for real singularities. References.