Surgery theory | Differential topology

H-cobordism

In geometric topology and differential topology, an (n + 1)-dimensional cobordism W between n-dimensional manifolds M and N is an h-cobordism (the h stands for homotopy equivalence) if the inclusion maps are homotopy equivalences. The h-cobordism theorem gives sufficient conditions for an h-cobordism to be trivial, i.e., to be C-isomorphic to the cylinder M × [0, 1]. Here C refers to any of the categories of smooth, piecewise linear, or topological manifolds. The theorem was first proved by Stephen Smale for which he received the Fields Medal and is a fundamental result in the theory of high-dimensional manifolds. For a start, it almost immediately proves the generalized Poincaré conjecture. (Wikipedia).

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Semi-s-cobordism | Topological manifold | Whitehead torsion | Groupoid | Hassler Whitney | Poincaré conjecture | Piecewise linear manifold | Millennium Prize Problems | Generalized Poincaré conjecture | Geometric topology | Ricci flow | Simple-homotopy equivalence | Henri Poincaré | Smooth structure | Cobordism | Differential topology | Manifold | Handle decomposition | 4-manifold | Whitney embedding theorem