James Waddell Alexander II (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. Events 335 - Dalmatius is raised to the rank of Caesar by his uncle Constantine I. Year 1888 ( MDCCCLXXXVIII) was a Leap year starting on Sunday (click on link for calendar of the Gregorian calendar (or a Events 1122 - Concordat of Worms. 1459 - Battle of Blore Heath, the first major battle of the English Year 1971 ( MCMLXXI) was a Common year starting on Friday (link will display full calendar of the 1971 Gregorian calendar. Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Algebraic topology is a branch of Mathematics which uses tools from Abstract algebra to study Topological spaces The basic goal is to find algebraic Events 335 - Dalmatius is raised to the rank of Caesar by his uncle Constantine I. Year 1888 ( MDCCCLXXXVIII) was a Leap year starting on Sunday (click on link for calendar of the Gregorian calendar (or a Events 1122 - Concordat of Worms. 1459 - Battle of Blore Heath, the first major battle of the English Year 1971 ( MCMLXXI) was a Common year starting on Friday (link will display full calendar of the 1971 Gregorian calendar. Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Oswald Veblen ( 24 June 1880 in Decorah Iowa &ndash 10 August, 1960) was an American Mathematician, Solomon Lefschetz ( 3 September 1884 – 5 October 1972) was an American Mathematician who did fundamental work on He was one of the first members of the Institute for Advanced Study (1933–1951), and also a professor at Princeton University (1920–1951). The Institute for Advanced Study, located in Princeton New Jersey, United States is a center for theoretical research Princeton University is a private Coeducational research university located in Princeton, New Jersey.

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. Algebraic topology is a branch of Mathematics which uses tools from Abstract algebra to study Topological spaces The basic goal is to find algebraic Jules Henri Poincaré ( 29 April 1854 &ndash 17 July 1912) (ˈʒyl ɑ̃ˈʁi pwɛ̃kaˈʁe was a French Mathematician In Mathematics, homology theory is the Axiomatic study of the intuitive geometric idea of homology of cycles on Topological spaces It can be broadly In Mathematics, specifically in Algebraic topology, cohomology is a general term for a Sequence of Abelian groups defined from a Cochain In Mathematics, a chain complex is a construct originally used in the field of Algebraic topology. For this, in 1928 he was awarded the Bôcher Memorial Prize. Year 1928 ( MCMXXVIII) was a Leap year starting on Sunday (link will display full calendar of the Gregorian calendar. The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1450 (contributed by 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. In Mathematics, knot theory is the area of Topology that studies mathematical knots While inspired by knots which appear in daily life in shoelaces In Mathematics, the Alexander polynomial is a Knot invariant which assigns a Polynomial with integer coefficients to each knot type In Mathematics, in particular Abstract algebra, a graded algebra is an Algebra over a field (or Commutative ring) with an extra piece of structure In Mathematics, the knot complement of a tame knot K is the set-theoretic complement of the interior of the embedding of a Solid torus From this invariant, he obtained the first polynomial knot invariant. In the mathematical field of Knot theory, a knot polynomial is a Knot invariant in the form of a Polynomial whose coefficients encode some of

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. In the mathematical area of Knot theory, a Reidemeister move refers to one of three local moves on a Link diagram. In Mathematics, knot theory is the area of Topology that studies mathematical knots While inspired by knots which appear in daily life in shoelaces

Alexander was also a noted mountaineer, having succeeded in many major ascents, e. “Alpinist” redirects here See also Alpinist (magazine Mountaineering is the Sport, Hobby or Profession of g. in the Swiss Alps and Colorado Rockies. The Swiss Alps (Schweizer Alpen Alpes suisses Alpi svizzere Alps svizras are the central portion of the Alps Mountain range that lies within 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. John White Alexander ( 7 October 1856 &ndash 31 May 1915) was an American portrait figure and decorative painter and 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. McCarthyism is a term describing the intense anti-communist suspicion in the United States in a period that lasted roughly from the late 1940s to the late 1950s 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

• O'Connor, John J. The Alexander horned sphere is one of the most famous pathological examples in Mathematics discovered in 1924 by J In Mathematics, the Alexander polynomial is a Knot invariant which assigns a Polynomial with integer coefficients to each knot type In Mathematics, particularly in Algebraic topology Alexander-Spanier cohomology is a Cohomology theory arising from Differential forms with In Mathematics, Alexander duality refers to a Duality theory presaged by a result of 1915 by J Alexander's trick, also known as the Alexander trick, is a basic result in Geometric topology, named after J & Robertson, Edmund F. , “James Waddell Alexander II”, MacTutor History of Mathematics archive 
• James Waddell Alexander II at the Mathematics Genealogy Project

References

• James, I. The MacTutor History of Mathematics archive is an award-winning website maintained by John J The Mathematics Genealogy Project is a web-based Database that gives an Academic genealogy based on Dissertation supervision relations 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.