Complex vs convex Morse functions and geodesic open books
| Autor: | Dehornoy, Pierre, Ozbagci, Burak |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Suppose that $\Sigma$ is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are three seemingly distinct constructions of open books on the unit (co)tangent bundle of $\Sigma$, having complex, contact, and dynamical flavors, respectively. Each one of these constructions is based on either an admissible divide or an ordered Morse function on $\Sigma$. We show that the resulting open books are pairwise isotopic provided that the ordered Morse function is adapted to the admissible divide on $\Sigma$. Moreover, we observe that if $\Sigma$ has positive genus, then none of these open books are planar and furthermore, we determine the only cases when they have genus one pages. Comment: Major revision. This is the final version, to appear in the International Journal of Mathematics |
| Databáze: | arXiv |
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