Poincaré and the early history of 3-manifolds

2012/07/23 by John Stillwell · 1 citation
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #History and Theory of Mathematics

paper · pdf · doi:10.1090/s0273-0979-2012-01385-x

openalex publication_date 2012/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27

Abstract

Recent developments in the theory of 3-manifolds, centered around the Poincaré conjecture, use methods that were not envisioned by Poincaré and his contemporaries. Nevertheless, the main themes of 3-manifold topology originated in Poincaré’s time. The purpose of this article is to reveal the origins of the subject by revisiting the world of the early topologists.

Citations

• Die beiden Kleeblattschlingen
• �ber die Topologie des dreidimensionalen Raumes
• Second Complément à l'Analysis Situs
• Sopra gli spazi di un numero qualunque di dimensioni
• �ber unendliche diskontinuierliche Gruppen
• On Computable Numbers, with an Application to the Entscheidungsproblem
• An Unsolvable Problem of Elementary Number Theory

Cited by

• Poincaré conjecture [wikipedia]

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