Canonical neighborhoods for topologically embedded polyhedra

Author:
Robert Craggs

Journal:
Trans. Amer. Math. Soc. **173** (1972), 465-490

MSC:
Primary 57C40; Secondary 57A10

DOI:
https://doi.org/10.1090/S0002-9947-1972-0394687-7

MathSciNet review:
0394687

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Abstract: D. R. McMillan has shown that in any neighborhood of a compact two sided surface in a -manifold there is a closed neighborhood of the surface which is the sum of a solid homeomorphic to the cartesian product of the surface with the unit interval and some small disjoint cubes-with-handles each of which intersects the cartesian product in a disk on its boundary. In the present paper the author generalizes this notion of canonical neighborhood so that it applies to topological embeddings of arbitrary polyhedra in -manifolds. This is done by replacing the cartesian products by small regular neighborhoods of polyhedral approximations to the topological embeddings.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0394687-7

Keywords:
-manifold,
neighborhoods of surfaces,
canonical neighborhoods,
topological embeddings of polyhedra,
small regular neighborhoods,
approximating polyhedra,
cubes-with-handles

Article copyright:
© Copyright 1972
American Mathematical Society