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On Embedding Essential Annuli in M3

Published online by Cambridge University Press:  20 November 2018

C. D. Feustel
C. D. Feustel*
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
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In [7; 8; 11] it is shown that an appropriate map of a planar surface into a 3-manifold can be replaced by an embedding. In [1 ; 4 ; 6 ; 7 ; 9 ; 10] conditions are given so that a "non-trivial" map of a planar surface (2-sphere) can be replaced by a non-trivial embedding of a planar surface (2-sphere). In this paper we give conditions on an annular map which guarantee the existence of a non-trivial embedding of an annulus. It is reported that F. Waldhausen has proved a similar but stronger "annulus theorem".

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1341 - 1350
Copyright
Copyright © Canadian Mathematical Society 1974

References

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