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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

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Graff G., Kaczkowska A.

Open Mathematics

2012

tom 10

nr 6

2160-2172

Let f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f. In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ℚ) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.

Ograniczanie wyników

1 Open Mathematics

1 Graff G.

1 Kaczkowska A.

1 2012

Wyniki wyszukiwania

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers