Laminated decompositions involving a given submanifold |
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Authors: | R.J. Daverman F.C. Tinsley |
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Affiliation: | Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA;Department of Mathematics, Colorado College, Colorado Springs, CO 80903, USA |
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Abstract: | Let M denote a connected (n+1)-manifold (without boundary). We study laminated decompositions of M, by which we mean upper semicontinous decompositions G of M into closed, connected n-manifolds. In particular, given M with a lamination G and N, a locally flat, closed, n-dimensional submanifold, we determine conditions under which M admits another lamination GN with N?GN. For n ≠ 3 a sufficient condition is that i: N → M be a homotopy equivalence. For n > 3 we give examples to show that i: N → M being a homology equivalence is not sufficient. We also show how to replace the assumption of local flatness of N with a weaker cellularity criterion (n ? 4) known as the inessential loops condition. We then give examples illustrating the abundance of pathology if M is not assumed to have a preexisting lamination. |
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Keywords: | Primary 57N15, 57N10, 54B15 Secondary 57N35, 57N80 |
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