Colin Rourke

Colin Rourke (born 1st Jan 1943) is a British mathematician, who has published papers in PL topology, low-dimensional topology, differential topology, group theory, relativity and cosmology. He is an emeritus professor at the Mathematics Institute of the University of Warwick and 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.

Most of Rourke's early work was carried out in collaboration with Brian Sanderson. They solved a number of outstanding problems: the provision of normal bundles for the PL category (which they called "Block bundles"), the non-existence of normal microbundles (top and PL) , and a geometric interpretation for all (generalized) homology theories (joint work with Sandro Buoncristiano, see bibliography).

Rourke was an invited speaker at ICM 1970.

From 1976-1981 Rourke was acting professor of pure mathematics at the Open University (on secondment from Warwick) where he masterminded the rewriting of the pure mathematics course.

In September 1986 Rourke and his graduate student, Eduardo Rêgo (later at University of Oporto), claimed to have solved the Poincaré Conjecture. 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.

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

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