The Story of the Higher Dimensional Poincaré Conjecture (What Actually Happened on the Beaches of Rio)

Steve Smale

Chapter 3 in From Topology to Computation: Proceedings of the Smalefest, 1993, pp 27-40 from Springer

Abstract: Abstract Although these pages tell mainly a personal story, let us start with a description of the “n-dimensional Poincaré Conjecture.” It asserts: A compact n-dimensional manifold M n that has the homotopy type of the n-dimensional sphere $$S^n = \{ x \in \mathbf{R}^{n + 1} \mathbf{|}\,\left\| x \right\| = 1\}$$ is homeomorphic to S n .

Keywords: National Science Foundation; Spectral Sequence; Differential Topology; Aegean Island; National Science Foundation Fund (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2740-3_3

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DOI: 10.1007/978-1-4612-2740-3_3

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