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Tubed incompressible surfaces in knot and link complements

✍ Scribed by Elizabeth Finkelstein; Yoav Moriah

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
260 KB
Volume
96
Category
Article
ISSN
0166-8641

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✦ Synopsis

We prove that the complements of all knots and links in S 3 which have a 2n-plat projection with absolute value of all twist coefficients bigger than 2 contain closed embedded incompressible nonboundary parallel surfaces. These surfaces are obtained from essential planar meridional surfaces by tubing to one side along the knot or link. In the case of a knot it follows that these surfaces stay incompressible in all manifolds obtained by non-trivial surgery on the knot.

πŸ“œ SIMILAR VOLUMES

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## Abstract The main purpose of this paper is to show that any embedding of __K~7~__ in three‐dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of __K~6~__ contains a pair of disjoint cycles which are homologically linked.