Combinatorial modifications of Reeb graphs and the realization problem
| Autor: | Michalak, Łukasz Patryk |
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| Rok vydání: | 2018 |
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| Zdroj: | Discrete Comput. Geom. 65 (2021), 1038-1060 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00454-020-00260-6 |
| Popis: | We prove that, up to homeomorphism, any graph subject to natural necessary conditions on orientation and the cycle rank can be realized as the Reeb graph of a Morse function on a given closed manifold $M$. Along the way, we show that the Reeb number $\mathcal{R}(M)$, i.e. the maximum cycle rank among all Reeb graphs of functions on $M$, is equal to the corank of fundamental group $\pi_1(M)$, thus extending a previous result of Gelbukh to the non-orientable case. Comment: 18 pages; The final publication is available at link.springer.com: https://doi.org/10.1007/s00454-020-00260-6 |
| Databáze: | arXiv |
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