Computing the Thurston-Bennequin invariant in open books
Sebastian Durst, Marc Kegel, and Mirko Klukas
TL;DR
This paper develops explicit formulas and algorithms for calculating the Thurston-Bennequin invariant of Legendrian knots in contact open books and Heegaard surfaces, extending to rationally nullhomologous knots in general 3-manifolds.
Contribution
It introduces new computational methods for the Thurston-Bennequin invariant applicable to a broad class of knots in various 3-manifolds.
Findings
Provided explicit formulas for Legendrian knots in open books.
Extended formulas to rationally nullhomologous knots in arbitrary 3-manifolds.
Developed algorithms for practical computation of the invariant.
Abstract
We give explicit formulas and algorithms for the computation of the Thurston-Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on contact Heegaard surfaces. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds.
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