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- W2550794586 abstract "In this chapter we state some interrelations between the topology of the ambient manifold (M^3) and dynamics of a diffeomorphism (fin MS(M^3)). These relation deal with the number $$g_{_f}=frac{r_{_f}-l_{_f}+2}{2},$$where (r_{_f}) is the number of the saddle periodic points and (l_{_f}) is the number of the knot periodic points of the diffeomorphism f. In the section 6.1 we construct the topological classification of closed orientable 3-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves. Such a manifold is either the 3-sphere if (g_{_f}=0) or the connected sum of (g_{_f}) copies of (mathbb S^2times mathbb S^1). We point out one more interrelation between (g_{_f}) and the topology of the manifold (M^3) if the diffeomorphism f is gradient-like and it has tamely embedded frames of 1-dimensional separatrices. In this case the ambient manifold (M^3) admits Heegaard splitting of genus (g_{_f}). The results of this chapter are for the most part contained in [1, 2]." @default.
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- W2550794586 date "2016-01-01" @default.
- W2550794586 modified "2023-09-28" @default.
- W2550794586 title "Interrelation Between the Dynamics of Morse–Smale Diffeomorphisms and the Topology of the Ambient 3-Manifold" @default.
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- W2550794586 doi "https://doi.org/10.1007/978-3-319-44847-3_6" @default.
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