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Closed incompressible surfaces in complements of wide knots and links

โœ Scribed by Martin Lustig; Yoav Moriah

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
806 KB
Volume
92
Category
Article
ISSN
0166-8641

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โœฆ Synopsis

We define the notion of wide knots (and links) and show that they contain closed incompressible nonboundary parallel surfaces in their complement. This is done by proving that these complements admit Heegaard splittings which are irreducible but weakly reducible, and using an extension of a result of Casson and Gordon. We then show that the class of wide knots and links is rather large, and that examples are easy to come by. We also show that the incompressible surfaces remain incompressible after most Dehn fillings.

๐Ÿ“œ SIMILAR VOLUMES

Tubed incompressible surfaces in knot an
Tubed incompressible surfaces in knot and link complements
โœ Elizabeth Finkelstein; Yoav Moriah ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 260 KB

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 tubin