James Waddell Alexander II

James Waddell Alexander II (* September 19, 1888, † September 23, 1971 ) was a topologist, a professor at Princeton University and one of the first members of the Institute for Advanced Study.

Life

Alexander came from a long-established Princeton family. He was the only child of the portrait painter John White Alexander and his wife Elizabeth. His grandfather was the president of a life insurance company and by wealth and education was the grandson of access to all levels of society open. 1917 Alexander married the Russian Natalia Levitzkaja.

He studied mathematics at Princeton and specialized in topology. He became a professor ( 1920-1951 ) and he coined, together with Oswald Veblen, Solomon Lefschetz and others, the development of topology in the United States in the era before the Second World War. In 1933 he was among the first members of the Institute for Advanced Study in Princeton (up to 1951). He gave a plenary lecture, Some Problems in Topology, at the International Congress of Mathematicians in Zurich in 1932.

Alexander was a passionate climber Alexander's Chimney, in Rocky Mountain National Park was named after him.

Towards the end of his life he withdrew from society. Alexander was an avowed socialist and it was observed by Joseph McCarthy's supporters suspicious. His last public act was signing a solidarity message for Robert Oppenheimer in 1954.

Work

J. W. Alexander was a pioneer of algebraic topology. He formed the homology theory on the foundations of Henri Poincaré and, based on the cohomology theory. In 1928 he received the Bôcher Memorial Prize for this achievement.

Then he laid the foundations of knot theory. He was named after him Alexander invariant, which is a module which is given by the homology of the cyclic superposition of Knotenkomplements, and finally the first polynomial knot invariant, which is now called the Alexander polynomial.

Along with Garland Briggs he was also a description of the knot invariants based on translations and knot diagrams.

Eponym

• Alexander sphere
• Alexander polynomial
• Alexander -Spanier cohomology
• Alexander duality