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Fibration theorems à la Milnor for analytic maps with non-isolated singularities
Mid Sweden University, Faculty of Science, Technology and Media, Department of Computer and Electrical Engineering (2023-). Universidade Federal da Paraíba, PB, João Pessoa, Brazil.
2024 (English)In: São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, E-ISSN 2316-9028, Vol. 18, p. 1178-1199Article in journal (Refereed) Published
Abstract [en]

We study the topology of real analytic maps in a neighborhood of a (possibly non-isolated) critical point. We prove fibration theorems à la Milnor for real analytic maps with non-isolated critical values. Here we study the situation for maps with arbitrary critical set. We use the concept of d-regularity introduced in an earlier paper for maps with an isolated critical value. We prove that this is the key point for the existence of a Milnor fibration on the sphere in the general setting. Plenty of examples are discussed along the text, particularly the interesting family of functions (f, g) : Rn→ R2 of the type (f,g)=(∑i=1naixip,∑i=1nbixiq), where ai, bi∈ R are constants in generic position and p, q≥ 2 are integers. 

Place, publisher, year, edition, pages
Springer Nature , 2024. Vol. 18, p. 1178-1199
Keywords [en]
d-regularity, Linear discriminant, Milnor fibration, Sub-analytic
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-49093DOI: 10.1007/s40863-023-00370-yISI: 001042579000001Scopus ID: 2-s2.0-85166581820OAI: oai:DiVA.org:miun-49093DiVA, id: diva2:1788906
Available from: 2023-08-17 Created: 2023-08-17 Last updated: 2024-12-10Bibliographically approved

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Menegon, Aurelio

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