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Complete topological invariant for Morse-Smale diffeomorphisms on 3-manifolds

O. V. Pochinka1

AnnotationThe present paper is devoted to topological classification of a set $G(M^3)$ of preserving orientation Morse-Smale diffeomorphisms $f$ given on smooth closed orientable 3-manifolds $M^3$. A complete topological invariant for a diffeomorphism $f\in G(M^3)$ is equivalence class of its scheme $S_f$, which contains an information on periodic dates and on topology of embedding in ambient manifold of two-dimensional invariant manifolds of the saddle periodic points of $f$. Moreover, it is introduced a set $\mathcal S$ of abstract schemes, having a representative from each equivalence class of schemes of the diffeomorphisms from $G(M^3)$ and it is constructed a diffeomorphism $f_S\in G(M^3)$ whose scheme is equivalent to $S$.
KeywordsMorse-Smale diffeomorphisms, topological classification, orbit space.

1Associate Professor of Theory Function Chair, Nizhny Novgorod State University after N.I. Lobachevsky, Nizhny Novgorod; olga-pochinka@yandex.ru.

Citation: O. V. Pochinka, "[Complete topological invariant for Morse-Smale diffeomorphisms on 3-manifolds]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,13:2 (2011) 17–24 (In Russian)