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arxiv: 1709.03328 · v1 · pith:VLC6F7RYnew · submitted 2017-09-11 · 🧮 math.GT · math.GN

Extending a Morse function to a non-orientable 3-manifold

Cl\'ement Laroche This is my paper
classification 🧮 math.GT math.GN
keywords functionbottlecollaringkleinnon-singularsolidboundarycondition
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Non-singular extensions of horizontal stable fold maps from surfaces to the plane

    math.GT 2024-10 unverdicted novelty 6.0

    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.

  2. Non-singular extensions of circle-valued Morse functions

    math.GT 2023-11 unverdicted novelty 5.0

    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.