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Picard–Lefschetz theory

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In mathematics, Picard–Lefschetz theory studies the topology of a complex manifold by looking at the critical points of a holomorphic function on the manifold. It was introduced by Émile Picard for complex surfaces in his book Picard & Simart (1897), and extended to higher dimensions by Lefschetz (1924). It is a complex analog of Morse theory that studies the topology of a real manifold by looking at the critical points of a real function. Deligne & Katz (1973) extended Picard–Lefschetz theory to varieties over more general fields, and Deligne used this generalization in his proof of the Weil conjectures.

Wikipedia Inglés http://en.wikipedia.org/wiki/Picard?Lefschetz_theory

Wikipedia Español http://es.wikipedia.org/wiki/Picard?Lefschetz_theory

Enlaces externos relacionado http://books.google.com/books?id=eqCyQgAACAAJ http://dx.doi.org/10.1016/0040-9383(81)90013-6 http://www.archive.org/details/thoriedesfoncti00simagoog