On reconstructing Morse functions with prescribed preimages on $3$-dimensional manifolds
Abstract
We discuss a necessary and sufficient condition for reconstruction of Morse functions with prescribed preimages on $3$-dimensional manifolds. The present work strengthens a previous result of the author where only sufficient conditions are studied. Our new work is also regarded as a kind of addendum.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2024
- DOI:
- arXiv:
- arXiv:2412.20626
- Bibcode:
- 2024arXiv241220626K
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- 7 pages. A kind of addenda to a published article http://mfat.imath.kiev.ua/article/?id=1911 (arXiv:2108.01300): here we show that the sufficient condition for reconstructing Morse functions there is also a necessary condition. This version is submitted to a refereed journal