- James Waddell Alexander II
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birth_date =September 19 ,1888
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death_date =September 23 ,1971
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field =topology
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known_for =algebraic topology
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footnotes =James Waddell Alexander II (
September 19 ,1888 –September 23 ,1971 ) was an importanttopologist of the pre-WWII era and part of an influential Princeton topology elite, which includedOswald Veblen ,Solomon Lefschetz , and others. He was one of the first members of theInstitute for Advanced Study (1933–1951), and also a professor atPrinceton University (1920–1951).He was a pioneer in
algebraic topology , setting the foundations forHenri Poincaré 's ideas onhomology theory and furthering it by foundingcohomology theory , which developed gradually in the decade after he gave a definition ofcochain . For this, in 1928 he was awarded theBôcher Memorial Prize . He also contributed to the beginnings ofknot theory by inventing theAlexander invariant of a knot, which in modern terms is agraded module obtained from the homology of acyclic covering of theknot complement . From this invariant, he obtained the firstpolynomial knot invariant .With Garland Briggs, he also gave a combinatorial description of knot invariance based on certain moves, now (against the history) called the
Reidemeister moves ; and also a means of computing homological invariants from theknot diagram .Alexander was also a noted
mountaineer , having succeeded in many major ascents, e.g. in theSwiss Alps and ColoradoRockies .Alexander's Chimney , in theRocky Mountain National Park , is named after him. When in Princeton, he liked to climb the university buildings, and always left his office window on the top floor ofFine Hall open so that he could enter by climbing the building.Alexander came from an old, distinguished Princeton family. He was the only child of the American portrait painter
John White Alexander and Elizabeth Alexander. His maternal grandfather, James Waddell Alexander, was the president of the Equitable Life Assurance Society. Alexander's affluence and upbringing allowed him to interact with high society in America and elsewhere. He married Natalia Levitzkaja in 1917, a Russian woman, and they would frequently spend time, until 1937, in the Chamonix area of France, where he would also climb.Towards the end of his life, he became a recluse. He was known as a socialist and his prominence brought him to the attention of McCarthyists. The atmosphere of the McCarthy era pushed him into greater seclusion. He was not seen in public after 1954, when he appeared to sign a letter supporting
Robert Oppenheimer .See also
*
Alexander horned sphere
*Alexander polynomial
*Alexander cochain
*Alexander-Spanier cohomology
*Alexander duality
*Alexander's trick External links
*MacTutor Biography|id=Alexander
*MathGenealogy |id=23944References
*James, I. M., Portrait of Alexander (1888--1971), Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 2, 123-129.
*Cohen, Leon W., James Waddell Alexander (1888-1971), Bull. Amer. Math. Soc. 79 (1973), 900--903.
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