Topological classification of circle-valued simple Morse-Bott functions on closed orientable surfaces

Erica Boizan Batista, João Carlos Ferreira Costa, and I.S. Meza-Sarmiento

Journal of Singularities
volume 25 (2022), 78-89

Received: 30 March 2021. Received in revised form: 28 May 2022.

DOI: 10.5427/jsing.2022.25d

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Abstract:

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.

2010 Mathematical Subject Classification:

58K15, 58K65, 58E05, 57R70

Key words and phrases:

Topological invariant, Morse-Bott functions, Reeb graph, topological equivalence

Author(s) information:

Erica Boizan Batista
Centro de Ciências e Tecnologia
Universidade Federal do Cariri
Juazeiro do Norte - CE, Brazil}
erica.batista@ufca.edu.br

João Carlos Ferreira Costa
Universidade Estadual Paulista (UNESP)
Instituto de Biociências, Letras e Ciências Exatas
Câmpus de São José do Rio Preto, Brazil
joao.costa@unesp.br

I.S. Meza-Sarmiento
Departamento de Matemática - UFSCar
Rod. Washington Luís, Km 235 - C.P. 676
CEP 13565-905 São Carlos
São Paulo, Brazil
isofia1015@gmail.com