Connected components of the space of circle-valued Morse functions on surfaces

Details Connected components of the space of circle-valued Morse functions on surfaces Connected components of the space of circle-valued Morse functions on surfaces

1999-06-05

arxiv.org/abs/math/9906031v2

Mathematics

Geometric Topology

10 pages, 1 figure

Scientific paper

We classify the path-components of the space of circle-valued Morse functions
on compact surfaces: two Morse functions $f, g: M\to S^1$ belong to same
path-component of this space if and only if they are homotopic and have equal
numbers of critical points at each index.

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