Solomon Lefschetz was a significant figure in the development of algebraic topology and its applications to various fields of mathematics. Here is detailed information about him:
Biography
- Birth: September 3, 1884, in Moscow, Russia.
- Death: October 5, 1972, in Princeton, New Jersey, USA.
- Immigration: Lefschetz moved to the United States at the age of 18, where he studied at Clark University and later at the University of Paris.
- Education: He earned his Ph.D. from Clark University in 1911.
- Accident: In 1917, Lefschetz lost both of his hands in an electrical accident. This event influenced his research focus towards theoretical aspects of mathematics, particularly topology.
Contributions to Mathematics
- Algebraic Topology: Lefschetz made pioneering contributions to algebraic topology. His work on the homology theory and the intersection theory in algebraic geometry were foundational.
- Lefschetz Fixed Point Theorem: One of his most famous results, this theorem states that if a continuous mapping from a compact topological space to itself has no fixed points, then its induced map on homology is the identity, plus a map with nonzero degree. This theorem has applications in various areas, including dynamical systems and physics.
- Lefschetz Pencil: He introduced the concept of the Lefschetz pencil, which is a tool used to study algebraic surfaces and their singularities.
- Books and Publications: Lefschetz authored several influential books, including "L'analysis situs et la géométrie algébrique" (1924), "Topology" (1930), and "Algebraic Topology" (1942).
Academic Career
- Clark University: He started his academic career at Clark University, where he was influenced by William Edward Story.
- Princeton University: After his accident, he moved to Princeton University, where he spent the majority of his career. He was instrumental in establishing the university as a center for topology research.
- Recognition: Lefschetz was awarded the Bôcher Memorial Prize in 1924, and he was elected to the National Academy of Sciences in 1928.
Legacy
- Influence: Lefschetz's work laid the groundwork for much of modern algebraic topology and influenced many mathematicians, including Henri Poincaré and Emmy Noether.
- Lefschetz Medal: The American Mathematical Society awards the Lefschetz Medal in his honor for outstanding contributions to topology or differential geometry.
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