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Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers
Abstract
Let f be a smooth self-map of an m-dimensional (m >3) closed connected and simply-connected manifold such that the sequence of the Lefschetz num- bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is constant for all suciently large r. We compute J[f] for self-maps of some manifolds with simple structure of homology groups.
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
Annales Polonici Mathematici
no. 107,
pages 29 - 48,
ISSN: 0066-2216 - Language:
- English
- Publication year:
- 2013
- Bibliographic description:
- Graff G., Kaczkowska A.: Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers// Annales Polonici Mathematici. -Vol. 107, nr. 1 (2013), s.29-48
- Verified by:
- Gdańsk University of Technology
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