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Milnor fibration th...
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Cisneros-Molina, Jose LuisUniv Nacl Autonoma Mexico, Unidad Cuernavaca, Inst Matemat, Ave Univ s n, Cuernavaca, Morelos, Mexico.
(författare)
Milnor fibration theorem for differentiable maps
- Artikel/kapitelEngelska2024
Förlag, utgivningsår, omfång ...
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Springer Nature,2024
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LIBRIS-ID:oai:DiVA.org:miun-50892
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https://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-50892URI
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https://doi.org/10.1007/s40687-024-00431-4DOI
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Språk:engelska
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Sammanfattning på:engelska
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Ämneskategori:ref swepub-contenttype
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Ämneskategori:art swepub-publicationtype
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In Cisneros-Molina et al. (Sao Paulo J Math Sci, 2023. https://doi.org/10.1007/s40863-023-00370-y) it was proved the existence of fibrations a la Milnor (in the tube and in the sphere) for real analytic maps f:(Rn,0)->(Rk,0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:({\mathbb {R}}<^>n,0) \rightarrow ({\mathbb {R}}<^>k,0)$$\end{document}, where n >= k >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge k\ge 2$$\end{document}, with non-isolated critical values. In the present article we extend the existence of the fibrations given in Cisneros-Molina et al. (Sao Paulo J Math Sci, 2023. https://doi.org/10.1007/s40863-023-00370-y) to differentiable maps of class Cl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>{\ell }$$\end{document}, l >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell \ge 2$$\end{document}, with possibly non-isolated critical value. This is done using a version of Ehresmann fibration theorem for differentiable maps of class Cl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>{\ell }$$\end{document} between smooth manifolds, which is a generalization of the proof given by Wolf (Michigan Math J 11:65-70, 1964) of Ehresmann fibration theorem. We also present a detailed example of a non-analytic map which has the aforementioned fibrations.
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Menegon, AurelioMittuniversitetet,Institutionen för ingenjörsvetenskap, matematik och ämnesdidaktik (2023-),Univ Fed Paraiba, Dept Matemat, Joao Pessoa, Paraiba, Brazil.(Swepub:miun)aurmen2200
(författare)
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Univ Nacl Autonoma Mexico, Unidad Cuernavaca, Inst Matemat, Ave Univ s n, Cuernavaca, Morelos, Mexico.Institutionen för ingenjörsvetenskap, matematik och ämnesdidaktik (2023-)
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Ingår i:Research in the Mathematical Sciences: Springer Nature11:22522-0144
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