Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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Minimal function on 3-manifolds with boundary

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Published Mar 1, 2020
DOI https://doi.org/10.15673/tmgc.v8i3-4.1619

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Nataliia Lukova-Chuiko
Taras Shevcheno National University of Kyiv
http://orcid.org/0000-0003-3224-4061

Abstract

We construct the complete topological invariant of minimal functions on the three-dimensional manifolds and proved the theorem about the implementation of this invariant feature. Thus, it is received the minimal topological classification of functions. Efficiency of constructed invariants is demonstrated by examples. We describe all the functions, the complexity of which does not exceed three.

Keywords:
Minimal function, topological equivalence, 3-manifolds, classification

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How to Cite
Lukova-Chuiko, N. (2020). Minimal function on 3-manifolds with boundary. Proceedings of the International Geometry Center, 8(3-4), 46-52. https://doi.org/10.15673/tmgc.v8i3-4.1619
Issue
Vol 8 No 3-4 (2015)
Section
Papers

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References

1. A.O. Prishlyak, The topological sructure of the functions with isolated critical points on 3-manifold // Algebras, Groups and Geometries, Vol. 32, No. 4, 2015.- pp. 400-422.
2. A. Prishlyak. Topological properties and functions on 2- and 3-manifolds. Palmarium Academic Publishing 2012. 132s.
3. V.M. Kuzakon, V.F.Kirichenko, A.O.Prishlyak. Smooth manifolds. Geometric and topological aspects // Proceedings of Inst Mathematics NAS of Ukraine. Mathematics and its applications. - 2013. - V. 97. 500 p.
4. N.V. Lukova-Chuiko, A.O. Prishlyak. M-layered equivalence of functions in general position on 3-manifolds with boundary // Journal of Computational and Applied Math. - 2011.- No.3 (106) - c.114-123.