James Waddell Alexander II

James Waddell Alexander II

Infobox Scientist
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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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James Waddell Alexander II (September 19, 1888September 23, 1971) was an important topologist of the pre-WWII era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others. He was one of the first members of the Institute for Advanced Study (1933–1951), and also a professor at Princeton University (1920–1951).

He was a pioneer in algebraic topology, setting the foundations for Henri Poincaré's ideas on homology theory and furthering it by founding cohomology theory, which developed gradually in the decade after he gave a definition of cochain. For this, in 1928 he was awarded the Bôcher Memorial Prize. He also contributed to the beginnings of knot theory by inventing the Alexander invariant of a knot, which in modern terms is a graded module obtained from the homology of a cyclic covering of the knot complement. From this invariant, he obtained the first polynomial 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 the knot diagram.

Alexander was also a noted mountaineer, having succeeded in many major ascents, e.g. in the Swiss Alps and Colorado Rockies. Alexander's Chimney, in the Rocky 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 of Fine 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=23944

References

*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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  • James Waddell Alexander — II (* 19. September 1888; † 23. September 1971) war ein bedeutender Topologe, Professor an der Princeton Universität und eines der ersten Mitglieder des Institute for Advanced Study. Inhaltsverzeichnis 1 Leben 2 Werk …   Deutsch Wikipedia

  • James Waddell Alexander II — (* 19. September 1888; † 23. September 1971) war ein bedeutender Topologe, Professor an der Princeton Universität und eines der ersten Mitglieder des Institute for Advanced Study. Inhaltsverzeichnis 1 Leben 2 Werk …   Deutsch Wikipedia

  • James Waddell Alexander II — Pour les articles homonymes, voir Alexander. James Waddell Alexander II est un mathématicien et topologue américain de l entre deux guerres, né le 19 septembre 1888 et mort le 23 septembre 1971. Il fait partie de l influente école de Princeton en …   Wikipédia en Français

  • Alexander, James Waddell, II — ▪ American mathematician born September 19, 1888, Sea Bright, New Jersey, U.S. died September 23, 1971, Princeton, New Jersey       American mathematician and a founder of the branch of mathematics originally known as analysis situs, now called… …   Universalium

  • James Alexander (Mathematiker) — James Waddell Alexander II (* 19. September 1888; † 23. September 1971) war ein bedeutender Topologe, Professor an der Princeton Universität und eines der ersten Mitglieder des Institute for Advanced Study. Inhaltsverzeichnis 1 Leben 2 Werk 2.1 …   Deutsch Wikipedia

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  • James Hazen Hyde — (1876 1959) was the son of Henry Baldwin Hyde, the founder of The Equitable Life Assurance Society of the United States. James Hazen Hyde was twenty three when he inherited the majority shares in the billion dollar Equitable Life Assurance… …   Wikipedia

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  • Alexander polynomial — In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a… …   Wikipedia

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