Name Colin Rourke | ||
Books A Geometric Approach to Homology Theory, Introduction to Piecewise-linear Topology | ||
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.
Contents
Career
Most of Rourke's early work, done in collaboration with B. J. Sanderson, was on "block bundles", also known as "stratified polyhedra". 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.
Poincare Conjecture
In September 1986 Rourke and his graduate student, Eduardo Rego (later at University of Oporto), claimed to have solved the Poincare 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 characterisation 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 Poincare Conjecture, if one existed.
In 2002, Martin Dunwoody posted a claimed proof of the Poincare Conjecture. Rourke identified its fatal flaw.