Homogeneity and extension properties of embeddings of in

Author:
Arnold C. Shilepsky

Journal:
Trans. Amer. Math. Soc. **195** (1974), 265-276

MSC:
Primary 57A10; Secondary 55A30

DOI:
https://doi.org/10.1090/S0002-9947-1974-0341494-9

MathSciNet review:
0341494

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Abstract | References | Similar Articles | Additional Information

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 orientation-preserving automorphisms of a simple closed curve is generalized.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0341494-9

Keywords:
Wild knot,
wild simple closed curve,
homogeneous embedding,
homogeneity

Article copyright:
© Copyright 1974
American Mathematical Society