Almost locally tame manifolds in a manifold
Author:
Harvey Rosen
Journal:
Trans. Amer. Math. Soc. 156 (1971), 5971
MSC:
Primary 54.78
MathSciNet review:
0275401
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Abstract: Several conditions are given which together imply that a 2manifold M in a 3manifold is locally tame from one of its complementary domains, U, at all except possibly one point. One of these conditions is that certain arbitrarily small simple closed curves on M can be collared from U. Another condition is that there exists a certain sequence of 2manifolds in U converging to M with the property that each unknotted, sufficiently small simple closed curve on each is nullhomologous on . Moreover, if each of these simple closed curves bounds a disk on a member of the sequence, then it is shown that M is tame from . As a result, if U is the complementary domain of a torus in that is wild from U at just one point, then U is not homeomorphic to the complement of a tame knot in .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197102754011
PII:
S 00029947(1971)02754011
Keywords:
Almost locally tame 2manifolds,
2manifolds in 3manifolds,
tameness from a complementary domain,
wildness from a complementary domain,
locally peripherally collared 2manifolds,
convergent sequence of 2manifolds,
locally spanned 2manifolds,
piercing disk,
almost locally polyhedral tori,
complements of tame knots
Article copyright:
© Copyright 1971 American Mathematical Society
