Computing rotation numbers in open books
arXiv:1801.01034
Abstract
We give explicit formulas and algorithms for the computation of the rotation number of a nullhomologous Legendrian knot on a page of a contact open book. On the way, we derive new formulas for the computation of the Thurston-Bennequin invariant of such knots and the Euler class and the d3-invariant of the underlying contact structure.
20 pages, 7 figures; v.2: minor changes and clarifications; v.3: changed Example 1.3 and corrected the definition of Q in Algorithm 6.1