LEGENDRIAN RIBBONS IN OVERTWISTED CONTACT STRUCTURES
2009 ◽
Vol 18
(04)
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pp. 523-529
Keyword(s):
The Self
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We show that a null-homologous transverse knot K in the complement of an overtwisted disk in a contact 3-manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self-linking number of K with respect to S satisfies sl (K, S) = -χ(S). In particular, every null-homologous topological knot type in an overtwisted contact manifold can be represented by the boundary of a Legendrian ribbon. Finally, we show that a contact structure is tight if and only if every Legendrian ribbon minimizes genus in its relative homology class.
1990 ◽
Vol 13
(3)
◽
pp. 545-553
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1978 ◽
Vol 82
(1-2)
◽
pp. 13-17
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2017 ◽
Vol 153
(9)
◽
pp. 1945-1986
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2009 ◽
Vol 11
(02)
◽
pp. 201-264
◽
Keyword(s):
2003 ◽
Vol 05
(04)
◽
pp. 569-627
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