Singular levels and topological invariants of Morse--Bott foliations on non orientable surfaces

José Martínez-Alfaro, Ingrid S. Meza-Sarmiento, Regilene D. S. Oliveira


We investigate the classification of closed curves and eight curves of saddle points defined on non-orientable closed surfaces, up to an ambient homeomorphism. The classification obtained here is applied to Morse-Bott foliations on non-orientable closed surfaces in order to define a complete topological invariant.


Morse-Bott functions; topological invariants; foliations; non-orientable surfaces

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