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