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arxiv: 1309.1866 · v1 · pith:H4YUQBTPnew · submitted 2013-09-07 · 🧮 math.GT · math.DG

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

classification 🧮 math.GT math.DG
keywords arc-diskcodimensiondisjointmanifoldpiecewisepropertyfactorsproperties
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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 $n\geq 4$ determined by general position properties, the piecewise disjoint arc-disk property is satisfied.

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