Colin P. Rourke

Colin Patrick Rourke (born 1943) is a British mathematician, specialising in low-dimensional topology, and emeritus professor at the Mathematics Institute of the University of Warwick. He is a founding editor of the journals Geometry & Topology and Algebraic & Geometric Topology, published by Mathematical Sciences Publishers, where he is the vice chair of its board of directors.^[1]

Career

Most of Rourke's early work, done in collaboration with B. J. Sanderson, was on "block bundles", also known as "stratified polyhedra".^[2] Their work was a reinvention of homology theory based on cobordism. A differential analogue would later be developed under the name "stratifold".

Rourke was an invited speaker at ICM 1970.^[3][4]

Poincaré Conjecture

In September 1986 Rourke and his graduate student, Eduardo Rêgo (later at University of Oporto), claimed to have solved the Poincaré Conjecture.^[5] Reaction by the topological community at the time was highly skeptical, and during a special seminar at University of California, Berkeley given by Rourke, a fatal error was found in the proof.^[6][7]

The part of the proof that was salvaged was a constructive characterisation and enumeration of Heegaard diagrams for homotopy 3-spheres.^[8] A later discovered algorithm of Rubinstein-Thompson identified when a homotopy 3-sphere was a topological 3-sphere.^[9] Together, the two algorithms provided an algorithm that would find a counterexample to the Poincaré Conjecture, if one existed.^[10]

In 2002, Martin Dunwoody posted a claimed proof of the Poincaré Conjecture.^[11] Rourke identified its fatal flaw.^[12][13][14]

Bibliography

• Rourke, C. P.; Sanderson, B. J. (1972). Introduction to piecewise-linear topology. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69. Springer-Verlag.
• Buoncristiano, S.; Rourke, C. P.; Sanderson, B. J (1976). A geometric approach to homology theory. London Mathematical Society Lecture Note Series, No. 18. Cambridge University Press.

References

1. "Board of Directors". Mathematical Sciences Publishers. Retrieved 8 October 2015.
2. Stone, David A. (1972). Stratified Polyhedra. Lecture Notes in Mathematics 252. Springer-Verlag.
3. "ICM Plenary and Invited Speakers since 1897". International Mathematical Union. Retrieved Oct 11, 2015.
4. Rourke, C. P. (1971). "Block structures in geometric and algebraic topology". Actes du Congrès International des Mathématiciens (Nice, 1970). Tome 2. Paris: Gauthier-Villars. pp. 127–32.
5. Gleick, James (30 September 1986). "One of Math's Major Problems Reported Solved". New York Times.
6. Szpiro, George G. (2007). Poincaré's Prize. Dutton. pp. 177–79. ISBN 978-0-525-95024-0.
7. O'Shea, Donal (2007). The Poincaré Conjecture. Walker Books. pp. 179–80. ISBN 978-0-8027-1532-6.
8. Rêgo, Eduardo; Rourke, Colin (1988). "Heegaard diagrams and homotopy 3-spheres". Topology. 27 (2): 137–43. doi:10.1016/0040-9383(88)90033-x.
9. The proof later of the Poincaré Conjecture simplified this to "always yes".
10. Rourke, Colin (1997). "Algorithms to disprove the Poincaré conjecture". Turkish Journal of Mathematics. 21 (1): 99–110.
11. Dunwoody, M. J. "A Proof of the Poincaré Conjecture ?" (PDF). Retrieved 9 October 2015.
12. "Math whiz tackles old problem with new twist". Sarasota Herald-Tribune. Apr 26, 2002. p. 6A.
13. Szpiro, George G. (2007). Poincaré's Prize. Dutton. pp. 181–82. ISBN 978-0-525-95024-0.
14. O'Shea, Donal (2007). The Poincaré Conjecture. Walker Books. p. 187. ISBN 978-0-8027-1532-6.

External links

• "Colin Rourke's WWW Homepage". Retrieved Oct 7, 2015.
• "Colin P. Rourke". Mathematics Genealogy Project. Retrieved Oct 7, 2015.