Rational linking and contact geometry

Details Rational linking and contact geometry Rational linking and contact geometry

2009-01-04

arxiv.org/abs/0901.0380v2

Mathematics

Symplectic Geometry

13 pages

Scientific paper

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 they are weakly Legendrian and transversely simple. This version of the paper corrects some typos and attributions to other papers.

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