Geodesic
Topological classification of circle-valued simple Morse-Bott functions on closed orientable surfaces
Journal of Singularities, Tome 25 (2022), pp. 78-89

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In this work we investigate the topological classification of circle-valued simple Morse-Bott functions on connected closed orientable surfaces, up to topological conjugacy. We provide a complete topological invariant, called the MB-Reeb graph. This invariant is based on the generalized Reeb graph and the topological type of singular level sets of these functions. The results presented here extend to those obtained by the authors in a previous work when the surface is the standard sphere.
DOI : 10.5427/jsing.2022.25d
Classification : 58K15, 58K65, 58E05, 57R70 
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     author = {Erica Boizan Batista and Jo\~ao Carlos Ferreira Costa, and I.S. Meza-Sarmiento},
     title = {Topological classification of circle-valued simple {Morse-Bott} functions on closed orientable surfaces},
     journal = {Journal of Singularities},
     pages = {78--89},
     publisher = {mathdoc},
     volume = {25},
     year = {2022},
     doi = {10.5427/jsing.2022.25d},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.25d/}
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Erica Boizan Batista; João Carlos Ferreira Costa,; I.S. Meza-Sarmiento. Topological classification of circle-valued simple Morse-Bott functions on closed orientable surfaces. Journal of Singularities, Tome 25 (2022), pp. 78-89. doi: 10.5427/jsing.2022.25d

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