Topological classification of circle-valued simple Morse-Bott functions

Journal of Singularities
volume 17 (2018), 388-402

Received: 20 April 2018. Received in revised form: 16 July 2018.

DOI: 10.5427/jsing.2018.17q

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Abstract:

In this work, we investigate the classification of Morse-Bott functions from S^2 to S^1, up to topological conjugacy. We give a complete topological invariant of simple Morse-Bott functions f:S^2 \to S^1. The invariant is based on the generalized Reeb graph associated to f (called here MB-Reeb graph). Moreover, a realization theorem is obtained.

Keywords:

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

2010 Mathematical Subject Classification:

58K15, 58K65, 58E05, 57R70

Author(s) information: