The recognition problem: What is a topological manifold?

DOI10.1090/S0002-9904-1978-14527-3zbMath0418.57005OpenAlexW1972864643MaRDI QIDQ3851298

James W. Cannon

Publication date: 1978

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9904-1978-14527-3

zbMATH Keywords

Antoine's necklaceAlexander's horned spheredouble suspension conjecturecharacterizing topological manifolds

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Generalized manifolds (57P99) Flatness and tameness of topological manifolds (57N45)

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Cites Work

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• Generalized Poincaré's conjecture in dimensions greater than four
• Tame Cantor sets in \(E^ 3\)
• Shrinking cell-like decompositions of manifolds. Codimension three
• Classification of simplicial triangulations of topological manifolds
• Every crumpled n-cube is a closed n-cell-complement
• The locally flat approximation of cell-like embedding relations
• Die beiden Dodekaederräume
• A topological H-cobordism theorem for \(n\geq 5\)
• Actions on \(S^ n\)
• Approximating cellular maps by homeomorphisms
• Embeddings of surfaces in \(E^ 3\)
• Generalization of a construction of Antoine
• Affine structures in 3-manifolds. V: The triangulation theorem and Hauptvermutung
• A homeomorphism between the 3-sphere and the sum of two solid horned spheres
• Singular homology theory
• A Surface Is Tame If Its Complement is 1-ULC
• Cell-like decompositions arising from mismatched sewings: applications to 4-manifolds
• Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88)
• Cell-like mappings and their generalizations
• Resolving zero-dimensional singularities in generalized manifolds
• Cell-Like, 0-Dimensional Decompositions of E 3
• Some Results on Crumpled Cubes
• A Characterization of Locally Euclidean Spaces
• Sums of Solid Horned Spheres
• A New Proof for the Hosay-Lininger Theorem About Crumpled Cubes
• Regular Neighbourhoods and the Stable Range
• ULC Properties in Neighbourhoods of Embedded Surfaces and Curves in E³
• Locally nice codimension one manifolds are locally flat
• A Characterization of 3-Space by Partitionings
• The Kline sphere characterization problem
• Locally peripherally euclidean spaces are locally euclidean