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Complete topological invariants of Morse-Smale flows and handle decompositions of 3-manifolds

Abstract

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.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 185–196, 2005.

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Prishlyak, A. Complete topological invariants of Morse-Smale flows and handle decompositions of 3-manifolds. J Math Sci 144, 4492–4499 (2007). https://doi.org/10.1007/s10958-007-0287-y

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Keywords

  • Manifold
  • Unstable Manifold
  • Critical Element
  • Stable Manifold
  • Homotopy Class