Computing rotation numbers in open books
Sebastian Durst, Marc Kegel
TL;DR
This paper provides explicit formulas and algorithms for computing the rotation number of nullhomologous Legendrian knots in contact open books, along with new formulas for related invariants.
Contribution
It introduces novel formulas and algorithms for calculating rotation numbers, Thurston-Bennequin invariants, and other contact invariants in open book decompositions.
Findings
Explicit formulas for rotation numbers of Legendrian knots.
Algorithms for computing Thurston-Bennequin invariants.
New formulas for Euler class and d3-invariant.
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology