A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces

Journal Article · Fri Oct 31 00:00:00 EDT 2014 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2014V205N10ABEH004423· OSTI ID:22364685

Grines, V Z; Pochinka, O V ^[1]; Kapkaeva, S Kh ^[2]

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1. N.I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod (Russian Federation)
2. N.P. Ogarev Mordovian State University, Saransk (Russian Federation)

In a paper of Oshemkov and Sharko, three-colour graphs were used to make the topological equivalence of Morse-Smale flows on surfaces obtained by Peixoto more precise. In the present paper, in the language of three-colour graphs equipped with automorphisms, we obtain a complete (including realization) topological classification of gradient-like cascades on surfaces. Bibliography: 25 titles.

• OSTI ID: 22364685
• Journal Information: Sbornik. Mathematics, Vol. 205, Issue 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CLASSIFICATION
COLOR
DIAGRAMS
GRAPH THEORY
MATHEMATICAL SOLUTIONS
SURFACES
TOPOLOGY