On combinatorial isotopy
John F. P. Hudson, Eric Christopher Zeeman (1964)
Publications Mathématiques de l'IHÉS
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John F. P. Hudson, Eric Christopher Zeeman (1964)
Publications Mathématiques de l'IHÉS
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H. Griffith, L. Howell (1969)
Fundamenta Mathematicae
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R. Bing (1959)
Fundamenta Mathematicae
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Jonathan P. Keiter (2008)
Visual Mathematics
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W. Jakobsche (1983)
Fundamenta Mathematicae
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Karol Borsuk, Anna Gmurczyk (1980)
Fundamenta Mathematicae
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David B. Gauld (1976)
Compositio Mathematica
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Chuichiro Hayashi, Koya Shimokawa (2001)
Revista Matemática Complutense
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We show that any Heegaard splitting of the pair of the solid torus (≅DxS) and its core loop (an interior point xS) is standard, using the notion of Heegaard splittings of pairs of 3-manifolds and properly imbedded graphs, which is defined in this paper.
Witold Rosicki (1990)
Fundamenta Mathematicae
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J. Stallings (1959)
Fundamenta Mathematicae
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Dušan Repovš, Arkady Skopenkov (2000)
Colloquium Mathematicae
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Suppose that P is a finite 2-polyhedron. We prove that there exists a PL surjective map f:Q → P from a fake surface Q with preimages of f either points or arcs or 2-disks. This yields a reduction of the Whitehead asphericity conjecture (which asserts that every subpolyhedron of an aspherical 2-polyhedron is also aspherical) to the case of fake surfaces. Moreover, if the set of points of P having a neighbourhood homeomorphic to the 2-disk is a disjoint union of open 2-disks, and every...