Poincaré's works leading to the Poincaré conjecture

DOI10.1007/s00407-021-00283-2zbMath1495.01015OpenAlexW3207076083WikidataQ113905162 ScholiaQ113905162MaRDI QIDQ2127584

Chang Wang, Lizhen Ji

Publication date: 20 April 2022

Published in: Archive for History of Exact Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00407-021-00283-2

zbMATH Keywords

Poincaré conjectureclassification of manifolds

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of mathematics in the 19th century (01A55) History of manifolds and cell complexes (57-03) History of algebraic topology (55-03)

Cites Work

• Henri Poincaré
• Poincaré's stated motivations for topology
• The problem of the invariance of dimension in the growth of modern topology. II
• The story of the higher dimensional Poincaré conjecture (what actually happened on the beaches of Rio)
• Historical evolution of the concept of homotopic paths
• Topologie dreidimensionaler gefaserter Räume
• Homotopieringe und Linsenräume
• Hidden harmony -- geometric fantasies. The rise of complex function theory
• Algorithmic homeomorphism of 3-manifolds as a corollary of geometrization
• The evolution of the concept of homeomorphism
• 3-manifold groups
• Uniformization of Riemann surfaces. Revisiting a hundred-year-old theorem. Translated from the French by Robert G. Burns
• The evolution of geometric structures on 3-manifolds
• The word problem and the isomorphism problem for groups
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Geometric Group Theory
• Poincaré and the early history of 3-manifolds
• The Geometries of 3-Manifolds
• Algorithmic topology and classification of 3-manifolds
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