Poincaré conjecture

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Poincaré conjecture

[‚pwän‚kä′rā kən‚jek·chər]
(mathematics)
The question as to whether a compact, simply connected three-dimensional manifold without boundary must be homeomorphic to the three-dimensional sphere.
References in periodicals archive ?
The extended entries include Pontrjagin's article on smooth manifolds and their application in homotopy theory; Thoms' work on global properties of differential manifolds; Novikov's paper on homotropy properties of Tom complexes; papers by Smale on the generalized Poincare's conjecture in dimensions greater than four and the structure of manifolds; Quillen's article on the formal group laws of unoriented and complex cobordism theory; Buchstaber, Mischenko and Novikov's joint effort on formal groups and their role in algebraic topological approaches; and Buchstaber and Novikov's work on formal groups, power systems and Adams operators.
Szpiro chronicles the history of Poincare's conjecture, the key events of the mathematician's life, and the many failed attempts to solve this topological problem.
Poincare's conjecture is one of the simplest possible questions to ask about three-dimensional spaces, yet it has stumped mathematicians from Poincare's time to the present.