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arXiv:1709.03328 [math.GT]AbstractReferencesReviewsResources

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

Clément Laroche

Published 2017-09-11Version 1

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.

Comments: Master thesis supervised by Thomas Fiedler
Categories: math.GT, math.GN
Subjects: 57M15, 58E05
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