Homogeneity and extension properties of embeddings of in
Author:
Arnold C. Shilepsky
Journal:
Trans. Amer. Math. Soc. 195 (1974), 265276
MSC:
Primary 57A10; Secondary 55A30
MathSciNet review:
0341494
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Abstract: Two properties of embeddings of simple closed curves in are explored in this paper. Let be a simple closed curve and an embedding of in . The simple closed curve S is homogeneously embedded or alternatively f is homogeneous if for any points p and q of S, there is an automorphism h of such that and . The embedding f or the simple closed curve S is extendible if any automorphism of S extends to an automorphism of . Two classes of wild simple closed curves are constructed and are shown to be homogeneously embedded. A new example of an extendible simple closed curve is constructed. A theorem of H. G. Bothe about extending orientationpreserving automorphisms of a simple closed curve is generalized.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197403414949
PII:
S 00029947(1974)03414949
Keywords:
Wild knot,
wild simple closed curve,
homogeneous embedding,
homogeneity
Article copyright:
© Copyright 1974
American Mathematical Society
