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.
Extending a Morse function to a non-orientable $3-$manifold
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Considering a solid 3-dimensional Klein bottle and a collaring of its boundary, can we extend a generic $C^\infty$ non-singular function defined on the collaring to the full solid Klein bottle without critical points? We give a condition on the Reeb graph of the given function that is necessary and sufficient for the existence of such a non-singular extension.
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math.GT 2verdicts
UNVERDICTED 2representative citing papers
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.
citing papers explorer
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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.