Products of cell-like decompositions

Daverman, Robert J.

doi:10.1016/0166-8641(80)90002-4

Cited by 15 publications

(9 citation statements)

References 58 publications

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“…If N is an n-manifold and H is a cell-like u.s.c. decomposition of N such that N/H is finite dimensional, then (N/H) x R5 is always an (n + 5)-manifold [6]. The next result indicates that there is such a stabilizing factor for a large class of decompositions of <7-manifolds.…”

Section: Preliminariesmentioning

confidence: 79%

Recognizing 𝜎-manifolds

Henderson¹

1985

Proc. Amer. Math. Soc.

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Section: Preliminariesmentioning

confidence: 79%

Recognizing 𝜎-manifolds

Henderson¹

1985

Proc. Amer. Math. Soc.

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“…It has the potential to lead to even further insights in demonstrating that all resolvable generalized manifolds of dimension n ≥ 4 are codimension one manifold factors or finding a counterexample, thereby solving the famous generalized R.L. Moore problem [4,15].…”

Section: Epiloguementioning

confidence: 99%

Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

Halverson

Repovš

2013

Open Mathematics

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Abstract:We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied. MSC: 57N15, 57N75, 57P99, 53C70Keywords

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“…Since then they have played an important role in various parts of topology, e.g. theory of transformation groups [4], theory of cell-like decompositions of manifolds [17], taming theory [12], suspensions of homology spheres [14], compactifications of open topological manifolds [8], manifold factors [15], etc.…”

Section: Generalized Manifoldsmentioning

confidence: 99%

“…S(X) = X, the singularities completely vanish upon multiplication of X by the real line, i.e. X x R is a genuine manifold -see [15]. )…”

Section: Generalized Manifoldsmentioning

confidence: 99%