Complex vs convex Morse functions and geodesic open books
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866915276368379904 |
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| author | Dehornoy, Pierre Ozbagci, Burak |
| author_facet | Dehornoy, Pierre Ozbagci, Burak |
| contents | Suppose that $Σ$ 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 $Σ$, 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 $Σ$. We show that the resulting open books are pairwise isotopic provided that the ordered Morse function is adapted to the admissible divide on $Σ$. Moreover, we observe that if $Σ$ has positive genus, then none of these open books are planar and furthermore, we determine the only cases when they have genus one pages. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2105_04814 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Complex vs convex Morse functions and geodesic open books Dehornoy, Pierre Ozbagci, Burak Geometric Topology Symplectic Geometry Suppose that $Σ$ 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 $Σ$, 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 $Σ$. We show that the resulting open books are pairwise isotopic provided that the ordered Morse function is adapted to the admissible divide on $Σ$. Moreover, we observe that if $Σ$ has positive genus, then none of these open books are planar and furthermore, we determine the only cases when they have genus one pages. |
| title | Complex vs convex Morse functions and geodesic open books |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2105.04814 |