J. W. Alexander: Difference between revisions

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J. W. Alexander may refer to:

J. W. Alexander (musician) (1916–1996), American gospel and soul singer, producer and entrepreneur
James Waddel Alexander (1804–1859), American Presbyterian minister and author
John White Alexander (1856–1915), American portrait painter and illustrator
James Waddell Alexander II (1888–1971), American mathematician and topologist

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-{{otherpeople|James Alexander}}
+'''J. W. Alexander''' may refer to:
+* [[J. W. Alexander (musician)]] (1916–1996), American gospel and soul singer, producer and entrepreneur
-[[Image:James_Waddell_Alexander.jpg|thumb|J. W. Alexander]]
+* [[James Waddel Alexander]] (1804–1859), American Presbyterian minister and author
+* [[John White Alexander]] (1856–1915), American portrait painter and illustrator
+* [[James Waddell Alexander II]] (1888–1971), American mathematician and topologist
+==See also==
-'''James Waddell Alexander''' ([[September 19]], [[1888]] – [[September 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).
+*[[James Alexander (disambiguation)]]
-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]].
+*[[John Alexander (disambiguation)]]
+{{hndis|Alexander, J.W.}}
-With [[Garland Briggs (mathematician)|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 [[McCarthyism|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]]
-==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.
-[[Category:1888 births|Alexander, J.W.]]
-[[Category:1971 deaths|Alexander, J.W.]]
-[[Category:20th century mathematicians|Alexander, J.W.]]
-[[Category:American mathematicians|Alexander, J.W.]]
-[[Category:Topologists|Alexander, J.W.]]
-[[Category:Princeton University faculty|Alexander, J.W.]]
-[[Category:Erdős number 4|Alexander, J.W.]]
-[[sl:James Waddell Alexander II.]]
-[[fi:James Waddell Alexander]]
-[[zh:詹姆斯·韋德爾·亞歷山大]]