TOPOLOGICAL CLASSIFICATION OF CIRCLE-VALUED SIMPLE MORSE-BOTT FUNCTIONS

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 -> 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.