Covering isotopies of in

Author:
Perrin Wright

Journal:
Proc. Amer. Math. Soc. **29** (1971), 591-598

MSC:
Primary 57.01

MathSciNet review:
0281215

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that a continuous family of locally flat separating embeddings of an -manifold into an *n*-manifold , where the family is parametrized by a locally compact finite-dimensional metric space *B*, can be covered locally and sometimes globally by a continuous family of homeomorphisms of onto itself, provided . Furthermore, the covering family can be chosen to extend a preassigned covering family corresponding to a compact connected subset of *B*. We derive a stronger result for embeddings of in , and show that the natural map from the space of orientation preserving homeomorphisms of to the space of locally flat embeddings of into , is a Serre fibration and a weak homotopy equivalence.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1971-0281215-4

Keywords:
Manifold,
locally flat embedding,
locally contractible,
completely regular mapping,
Serre fibration,
weak homotopy equivalence

Article copyright:
© Copyright 1971
American Mathematical Society