TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → 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(Σ) of the cur...
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Trường Đại học Đà Lạt
2023
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/114441 https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/864 |
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oai:scholar.dlu.edu.vn:DLU123456789-1144412023-10-27T14:46:54Z TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3 Javier, Fernández de Bobadilla Guillermo, Peñafort-Sanchis José, Edson Sampaio 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 → S^5 associated to finitely determined map germs (C^2 , 0) → (C^3 , 0). 2023-03-04T08:26:15Z 2023-03-04T08:26:15Z 2022 Article 0866-787X https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/114441 https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/864 10.37569/DalatUniversity.12.2.864(2022) en Tạp chí Khoa học Đại học Đà Lạt, Tập 12, Số 2; tr. 19-25 application/pdf Trường Đại học Đà Lạt |
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Thư viện Trường Đại học Đà Lạt |
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English |
| 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 → S^5 associated to finitely determined map germs (C^2 , 0) → (C^3 , 0). |
| format |
Article |
| author |
Javier, Fernández de Bobadilla Guillermo, Peñafort-Sanchis José, Edson Sampaio |
| spellingShingle |
Javier, Fernández de Bobadilla Guillermo, Peñafort-Sanchis José, Edson Sampaio TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3 |
| author_facet |
Javier, Fernández de Bobadilla Guillermo, Peñafort-Sanchis José, Edson Sampaio |
| author_sort |
Javier, Fernández de Bobadilla |
| title |
TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3 |
| title_short |
TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3 |
| title_full |
TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3 |
| title_fullStr |
TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3 |
| title_full_unstemmed |
TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3 |
| title_sort |
topological invariants and milnor fiber for a-finite germs c^2 → c^3 |
| publisher |
Trường Đại học Đà Lạt |
| publishDate |
2023 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/114441 https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/864 |
| _version_ |
1781718789211029504 |