TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\)
This note is the observation that a simple combination of known results shows that the usual analytic invariants of a finitely determined multi-germ \(f : (C^2 , S) → (C^3 , 0) \)—namely, the image Milnor number , the number of cross-caps and triple points, \(C\) and \(T\), and the Milnor number \(μ...
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| Language: | English |
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Dalat University
2022-01-01
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| Series: | Tạp chí Khoa học Đại học Đà Lạt |
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| Online Access: | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/864 |
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| author | Javier Fernández De Bobadilla Guillermo Peñafort-Sanchis José Edson Sampaio |
| author_facet | Javier Fernández De Bobadilla Guillermo Peñafort-Sanchis José Edson Sampaio |
| author_sort | Javier Fernández De Bobadilla |
| collection | DOAJ |
| description | This note is the observation that a simple combination of known results shows that the usual analytic invariants of a finitely determined multi-germ \(f : (C^2 , S) → (C^3 , 0) \)—namely, the image Milnor number , the number of cross-caps and triple points, \(C\) and \(T\), and the Milnor number \(μ(Σ)\) of the curve of double points in the target—depend only on the embedded topological type of the image of \(f\). As a consequence, one obtains the topological invariance of the sign-refined Smale invariant for immersions \(j : S^3 \looparrowright S^5\) associated to finitely determined map germs \((C^2 , 0) → (C^3 , 0)\). |
| format | Article |
| id | doaj-art-d90fab783e7d42b297de989b29a9121a |
| institution | Kabale University |
| issn | 0866-787X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Dalat University |
| record_format | Article |
| series | Tạp chí Khoa học Đại học Đà Lạt |
| spelling | doaj-art-d90fab783e7d42b297de989b29a9121a2025-02-02T23:31:55ZengDalat UniversityTạp chí Khoa học Đại học Đà Lạt0866-787X2022-01-01192510.37569/DalatUniversity.12.2.864(2022)622TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\)Javier Fernández De Bobadilla0Guillermo Peñafort-Sanchis1José Edson Sampaio2Basque Foundation for ScienceMazarredo, BilbaoUniversidade Federal do Ceará, Rua Campus do PiciThis note is the observation that a simple combination of known results shows that the usual analytic invariants of a finitely determined multi-germ \(f : (C^2 , S) → (C^3 , 0) \)—namely, the image Milnor number , the number of cross-caps and triple points, \(C\) and \(T\), and the Milnor number \(μ(Σ)\) of the curve of double points in the target—depend only on the embedded topological type of the image of \(f\). As a consequence, one obtains the topological invariance of the sign-refined Smale invariant for immersions \(j : S^3 \looparrowright S^5\) associated to finitely determined map germs \((C^2 , 0) → (C^3 , 0)\).https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/864milnor fibertopological invariance. |
| spellingShingle | Javier Fernández De Bobadilla Guillermo Peñafort-Sanchis José Edson Sampaio TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\) Tạp chí Khoa học Đại học Đà Lạt milnor fiber topological invariance. |
| title | TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\) |
| title_full | TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\) |
| title_fullStr | TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\) |
| title_full_unstemmed | TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\) |
| title_short | TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\) |
| title_sort | topological invariants and milnor fibre for mathcal a finite germs c 2 to c 3 |
| topic | milnor fiber topological invariance. |
| url | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/864 |
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