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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 8 and homology groups with the sum of ranks less or equal to 10
Opis
An important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 8 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f. For sufficiently large r the invariant Jr[f] is independent of the choice of r and in that case it is natural to write J[f] instead of Jr[f]. We provide the values of the simplified version of the invariant: J[f] (mod 2) (which is equal either J[f] or J[f]+1) for manifolds of dimension 8 having the sum of ranks of homology groups less or equal 10. The results are based on the combinatorial scheme for computing J[f] introduced in “Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers” by G. Graff and A. Kaczkowska, [Cent. Eur. J. Math., 10(6), 2012, 2160-2172, https://doi.org/10.2478/s11533-012-0122-7]. The data contains text files of the form J[vector_of_ranks _of_homology_groups].txt. Each file consists of all possible triples, structured as follows: the first position contains a sequence of lists, where the i-th list corresponds to the degrees of non-zero eigenvalues of the i-th induced homomorphism, the second position contains a set of non-zero periodic expansion coefficients, the third position contains corresponding value of the invariant J[f].
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otwiera się w nowej karcie
CC BYUznanie autorstwa
Informacje szczegółowe
- Rok publikacji:
- 2020
- Data zatwierdzenia:
- 2020-12-17
- Język danych badawczych:
- angielski
- Dyscypliny:
-
- matematyka (Dziedzina nauk ścisłych i przyrodniczych)
- DOI:
- Identyfikator DOI 10.34808/pw16-z682 otwiera się w nowej karcie
- Weryfikacja:
- Politechnika Gdańska
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