The Poincaré Conjecture and Related Statements

DOI10.1007/978-3-030-13609-3_17zbMath1454.57001OpenAlexW4210984963MaRDI QIDQ5129781

Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 23 October 2020

Published in: Geometry in History (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-13609-3_17

zbMATH Keywords

triangulationconehomotopy groupspherefundamental groupconnected sumintersection formsuspensionmapping class groupHeegaard splittingsHaken manifoldcombinatorial triangulationBusemann \(G\)-spacemanifold recognition problemsmooth manifoldprime decompositionPoincaré conjectureclosed 3-manifoldhomeomorphism problemtopological manifoldThurston geometrization conjectureSeifert-van Kampen theoremtriangulation conjectureclosed simply connected 4-manifoldBing-Borsuk problem(Non)PL-conjecture(Non)smoothable manifold(Non)triangulable manifoldAlexandrov space with curvature bounded aboveJSJ-splitting theoremsplitting homomorphism

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) History of manifolds and cell complexes (57-03) PL-topology (57Q99) Homotopy spheres, Poincaré conjecture (57R60) General topology of 3-manifolds (57K30)

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