Existence of non-singular extensions for horizontal stable fold maps equals existence of pairing maps, plus Euler characteristic and fundamental group computations for the 3-manifolds.
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Necessary and sufficient conditions are provided for non-singular extensions of circle-valued Morse functions from closed orientable surfaces to compact orientable 3-manifolds, given a collar submersion.
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Non-singular extensions of horizontal stable fold maps from surfaces to the plane
Existence of non-singular extensions for horizontal stable fold maps equals existence of pairing maps, plus Euler characteristic and fundamental group computations for the 3-manifolds.
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Non-singular extensions of circle-valued Morse functions
Necessary and sufficient conditions are provided for non-singular extensions of circle-valued Morse functions from closed orientable surfaces to compact orientable 3-manifolds, given a collar submersion.