On Milnor’s fibration theorem and its offspring after 50 years
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Abstract:
Milnor’s fibration theorem is about the geometry and topology of real and complex analytic maps near their critical points, a ubiquitous theme in mathematics. As such, after 50 years, this has become a whole area of research on its own, with a vast literature, plenty of different viewpoints, a large progeny, and connections with many other branches of mathematics. In this work we revisit the classical theory in both the real and complex settings, and we glance at some areas of current research and connections with other important topics. The purpose of this article is twofold. On the one hand, it should serve as an introduction to the topic for nonexperts, and on the other hand, it gives a wide perspective of some of the work on the subject that has been and is being done. It includes a vast literature for further reading.References
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Additional Information
- José Seade
- Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Cuidad Universitaria, 04510 Coyoacan, Mexico
- MR Author ID: 157790
- Email: jseade@im.unam.mx
- Received by editor(s): June 15, 2018
- Published electronically: November 8, 2018
- Additional Notes: The author’s research was partially supported by CONACYT 282937, PAPIIT-UNAM IN 110517, and CNRS-UMI 2001, Laboratoire Solomon Lefschetz-LaSoL, Cuernavaca, Mexico.
- © Copyright 2018 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 56 (2019), 281-348
- MSC (2010): Primary 32SXX, 14BXX, 57M27, 57M50; Secondary 32QXX, 32JXX, 55S35, 57R20, 57R57, 57R77
- DOI: https://doi.org/10.1090/bull/1654
- MathSciNet review: 3923346
Dedicated: To Jack, whose profoundness and clarity of vision seep into our appreciation of the beauty and depth of mathematics.