José Luis Cisneros-Molina

Wednesday, September 23rd, 2020. Gmeet at 4:20 pm

**Title: Exotic spheres and the birth of Milnor’s Fibration Theorem **

**Abstract**: Milnor’s fibration theorem is a landmark in singularity theory, it allows to

deepen the study of the geometry and topology of analytic maps near their critical

points. To each singular point of a complex hypersurface it associates a fibre bundle,

known as the Milnor Fibration of the singularity. The birth of Milnor's Fibration Theorem is a curious story, since its origin is not in

Singularity Theory. It begins with the discovery by Milnor in 1956 of the first "exotic spheres": smooth

7-manifolds homeomorphic to the standard 7-sphere, but with non-equivalent differentiable structures. Later, work of some great

mathematicians like Brieskorn, Jänich, Hirzebruch and Pham, led to the discovery of some examples of complex hypersurface singularities whose

links are exotic spheres. This motivated Milnor to determine when the link of a complex hypersurface

singularity is a homotopy sphere, culminating in his now famous book "Singular points of complex hypersurfaces". One of the main results is

precisely Milnor's Fibration Theorem. The aim of this non-technical talk is to tell this interesting story.