Mathematician:James Waddell Alexander II

American mathematician who did pioneering work in topology and knot theory.

Nationality
American

History

 * Born: 19 Sept 1888, Sea Bright, New Jersey, USA
 * Died: 23 Sept 1971, Princeton, New Jersey, USA

Theorems and Definitions

 * Alexander Horned Sphere
 * Antoine Horned Sphere (based on Antoine's Necklace by Louis Antoine)
 * Alexander Polynomial
 * Alexander Cochain
 * Alexander-Spanier Cohomology (with Edwin Henry Spanier)
 * Alexander Duality
 * Alexander's Trick
 * Alexander-Conway Polynomial (with John Horton Conway) (a variant of the Alexander Polynomial)
 * Alexander Invariant
 * Alexander Matrix
 * Alexander Module
 * Alexander Ideal
 * Alexander's Compactness Theorem, also known as the Alexander Sub-Basis (or Subbase) Theorem

Books and Papers

 * 1915: Functions which map the interior of the unit circle upon simple regions
 * 1924: An Example of a Simply Connected Surface Bounding a Region which is not Simply Connected: Proceedings of the National Academy of Sciences 10 (1): 8–10 (in which the Alexander Horned Sphere is introduced)
 * 1924: Remarks on a Point Set Constructed by Antoine: Proceedings of the National Academy of Sciences 10 (1): 10–12 (in which the Antoine Horned Sphere is introduced)
 * 1926: Combinatorial analysis situs
 * 1928: Topological invariants of knots and links
 * 1935: On the Chains of a Complex and Their Duals: Proceedings of the National Academy of Sciences 21 (8): 509–511