Teorema de Poincaré-Hopf
2019; Lázaro, C. and Rodrigues, T.; Volume: 16; Linguagem: Inglês
10.21167/cqdvol16201923169664jpbntbt134162
ISSN2316-9664
AutoresJean‐Paul Brasselet, Nguyễn Thị Bích Thủy,
Tópico(s)Advanced Mathematical Theories
ResumoThe Poincaré-Hopf Theorem is one of the mathematical results which are the most used not only in mathematics but also in other fields of sciences (Physics, Chemistry, Biology and even Economy, Psychology, etc.).The Poincaré-Hopf Theorem connects a combinatoric invariant: the Euler-Poincaré characteristic with objects of differential geometry, namely indices of vector fields.There are many proofs of the Theorem, one of the most well-known due to Milnor uses vectorfields with non-degenerate isolated singularities.In this paper, using the radial extension technique of Marie-Hélène Schwartz, we show that the Milnor proof can be used for any vectorfield with isolatd singularities of any index.
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