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The Unique Decomposition Theorem for 3-Manifolds Admitting Morse–Smale Diffeomorphisms without Heteroclinic Curves

Moscow Mathematical Journal. 2025. Vol. 25. No. 1. P. 79–90.
Eugene Osenkov, Pochinka O.

One of the fundamental results of three-dimensional topology is the Kneser–Milnor unique decomposition theorem. If a 3-manifold admits a Morse–Smale diffeomorphism without heteroclinic curves, the topology of the decomposition summands can be substantially refined. For orientable 3-manifolds this was done by C. Bonatti, V.Z. Grines, V.S. Medvedev and E. Pecou in 2002. In the present paper, we obtain an exhaustive description of the decomposition into a connected sum of non-orientable 3-manifolds admitting Morse–Smale diffeomorphisms without heteroclinic curves.

Research target: Mathematics
Language: English
Full text
DOI
Keywords: invariant manifoldshyperbolic dynamicsгетероклинические орбитытопология несущего многообразияheteroclinic orbitsдиффеоморфизмы Морса-Смейла Morse-Smale diffeomorphismинвариантные многообразиягиперболическая динамикаambient manifold topology
Publication based on the results of:
Differential-geometric properties of dynamical systems and mathematical modeling of processes (2025)
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