Approximating topological surfaces in -manifolds

Author:
Gerard A. Venema

Journal:
Trans. Amer. Math. Soc. **265** (1981), 35-45

MSC:
Primary 57Q35; Secondary 57N45

DOI:
https://doi.org/10.1090/S0002-9947-1981-0607105-3

MathSciNet review:
607105

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Abstract: Let be a compact, connected -manifold with and let be a topological embedding of into a -manifold. The main theorem of this paper asserts that if is a piecewise linear -manifold, then can be arbitrarily closely approximated by locally flat PL embeddings. It is also shown that if the -dimensional annulus conjecture is correct and if is a topological -manifold, then can be arbitrarily closely approximated by locally flat embeddings. These results generalize the author's previous theorems about approximating disks in -space.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0607105-3

Keywords:
Surface,
-manifold,
topological embedding,
piecewise linear approximation,
locally flat approximation

Article copyright:
© Copyright 1981
American Mathematical Society