| Solomon Lefschetz |
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He was badly injured in an industrial accident in 1907, losing both hands. He moved towards mathematics, receiving a Ph.D. in algebraic geometry from Clark University in Worcester, Massachusetts in 1911. He then took positions in Nebraska and Kansas, moving to Princeton in 1924, where he was soon given a permanent position. He remained there until 1953. In the application of topology to algebraic geometry, he followed the work of Charles Émile Picard , whom he had heard lecture in Paris. He proved theorems on the topology of Hyperplane sections of algebraic varieties, which provide a basic inductive tool (these are now seen as allied to Morse Theory , though a Lefschetz Pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other). The Picard-Lefschetz Formula in the theory of Vanishing Cycle s is a basic tool relating the Degeneration of families of varieties with 'loss' of topology, to Monodromy . His book ''L'analysis situs et la géométrie algébrique'' from 1924, though opaque foundationally given the current technical state of Homology Theory , was in the long term very influential (one could say that it was one of the sources for the eventual proof of the Weil Conjectures , through SGA7 ). In 1924 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. The s. He was editor of ''the Annals Of Mathematics '' from 1928 to 1958. During this time, ''Annals'' became an increasingly well-known and respected journal, and Lefschetz played an important role in this. The rise of ''Annals'', in turn, stimulated American mathematics. See also: Lefschetz Hyperplane Theorem , Lefschetz Duality . EXTERNAL LINKS |
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