# Mathematician:James Waddell Alexander II

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## Contents

## Mathematician

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 Alexander's Sub-Basis (or Subbase) Theorem

Results named for **James Waddell Alexander II** can be found here.

Definitions of concepts named for **James Waddell Alexander II** can be found here.

## Publications

- 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***Vol. 10 (1)**: pp. 8 – 10) (in which the definition of Alexander Horned Sphere is presented) - 1924:
*Remarks on a Point Set Constructed by Antoine*(*Proceedings of the National Academy of Sciences***Vol. 10 (1)**: pp. 10 – 12) (in which the definition of Antoine Horned Sphere is presented) - 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***Vol. 21 (8)**: pp. 509 – 511)

## Sources

- John J. O'Connor and Edmund F. Robertson: "James Waddell Alexander II": MacTutor History of Mathematics archive

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**Alexander's sub-base theorem**