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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Approximating topological surfaces in $4$-manifolds
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by Gerard A. Venema PDF
Trans. Amer. Math. Soc. 265 (1981), 35-45 Request permission

Abstract:

Let ${M^2}$ be a compact, connected $2$-manifold with $\partial {M^2} \ne \emptyset$ and let $h:{M^2} \to {W^4}$ be a topological embedding of ${M^2}$ into a $4$-manifold. The main theorem of this paper asserts that if ${W^4}$ is a piecewise linear $4$-manifold, then $h$ can be arbitrarily closely approximated by locally flat PL embeddings. It is also shown that if the $4$-dimensional annulus conjecture is correct and if $W$ is a topological $4$-manifold, then $h$ can be arbitrarily closely approximated by locally flat embeddings. These results generalize the author’s previous theorems about approximating disks in $4$-space.
References
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • 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