Complete topological invariants of Morse-Smale flows and handle decompositions of 3-manifolds
- 64 Downloads
We construct a topological invariant for the canonical decomposition on prime and round handles associated with a Morse-Smale flow on a closed 3-manifold. We prove that the flows are topologically equivalent if and only if their invariants coincide.
KeywordsManifold Unstable Manifold Critical Element Stable Manifold Homotopy Class
Unable to display preview. Download preview PDF.
- 1.V. S. Afraimovich and L. P. Shilnikov, “On singular sets of Morse-Smale systems,” Tr. Mosk. Mat. Obshch., 28, 181–214 (1973).Google Scholar
- 5.D. Asimov, “Notes on the topology of vector fields and flows,” in: Visualization 93, San Jose, CA (1993), pp. 1–23.Google Scholar
- 7.C. Bonatti and R. Langevin, Difféomorphismes de Smale des Surfaces, Soc. Math. France, Vol. 250, Astérisque, Paris (1998).Google Scholar
- 11.M. Peixoto, “On the classification of flows on two-manifolds,” in: M. Peixoto, ed., Dynamical Systems, Academic Press (1973), pp. 389–419.Google Scholar
- 16.A. O. Prishlyak, “Topological equivalence of functions and Morse-Smale vector fields on 3-manifolds, ” in: Topology and Geometry. Proc. Ukrainian Math. Congress, 2001, Kiev (2003), pp. 29–38.Google Scholar
- 18.Ya. L. Umanskii, “Necessary and sufficient conditions for the topological equivalence of three-dimensional Morse-Smale dynamical systems with a finite number of singular trajectories,” Mat. Sb., 181, No. 2, 212–239 (1990).Google Scholar
- 19.I. Vlasenko, “Complete invariant for Morse-Smale diffeomorphisms on 2-manifolds,” in: V. V. Sharko, ed., Some Problems of Modern Math., Vol. 25, Kiev Mat. Inst. (1998), pp. 60–93.Google Scholar