Abstract: I will survey some of the classical developments in combinatorial
topology, motivated in particular by the Poincare conjecture, and related
questions. Among other things, I will discuss
-- The origin of Poincare's famous conjecture, and homology spheres.
-- The approach of Whitehead, his failed proof attempt and contractible manifolds.
-- The approach of Zeeman, and the results of Cohen, Gillman-Rolfsen and others.
-- The generalized Poincare conjecture, and the work of Stallings, Zeeman and Newman.
-- Non-PL spheres, and the work of Edwards and Cannon.