On Suspensions Over Gradient-Like Diffeomorphisms of Surfaces with Three Periodic Orbits

S. Smale showed that suspensions over conjugate diffeomorphisms are topologically equivalent. Under certain assumptions, the conjugacy of diffeomorphisms is equivalent to the equivalence of suspensions. We show that this criterion holds for gradient-like diffeomorphisms with three periodic orbits on...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.284 (1), p.4-16
Main Authors: Baranov, D. A., Pochinka, O. V., Shubin, D. D., Yakovlev, E. I.
Format: Article
Language:English
Subjects:
Equivalence
Homology
Isomorphism
Manifolds
Mathematics
Mathematics and Statistics
Orbits
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Summary:S. Smale showed that suspensions over conjugate diffeomorphisms are topologically equivalent. Under certain assumptions, the conjugacy of diffeomorphisms is equivalent to the equivalence of suspensions. We show that this criterion holds for gradient-like diffeomorphisms with three periodic orbits on arbitrary orientable surfaces, prove that 3-manifolds admitting suspensions over such diffeomorphisms are small Seifert manifolds, and calculate the homology groups of these manifolds and the number of equivalence classes of flows on each admissible Seifert manifold.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07325-4