Moscow Mathematical Journal

Volume 25, Issue 1, January–March 2025 pp. 79–90.

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

Authors: Eugene Osenkov (1) and Olga Pochinka (1)
Author institution:(1) Department of Fundamental Mathematics, HSE N. Novgorod, Bol’shaya Pecherskaya st., 25/12, Nizhny Novgorod, 603155, N. Novgorod Region, Russia

Summary:

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.

2020 Math. Subj. Class. 37D15, 37C05, 57R50.

Keywords: Morse–Smale diffeomorphisms, ambient manifold topology, invariant manifolds, heteroclinic orbits, hyperbolic dynamics, prime decomosition for 3-manifolds.

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