Rational linking and contact geometry

By Kenneth L. Baker, John B. Etnyre. 2009

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In the note we study Legendrian and transverse knots in rationally null-homologous knot types. In particular, we generalize the standard definitions of self-linking number, Thurston–Bennequin invariant, and rotation number. We then prove a version of Bennequin’s inequality for these knots and classify precisely when the Bennequin bound is sharp for fibered knot types. Finally, we study rational unknots and show that they are weakly Legendrian and transversely simple.

Subfields: Genetics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/427a457c0a2e78ae06997eb18e5bdfdbbba4e5a6