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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
Description
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].
Dataset file
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.Example script for calculation:
https://github.com/antespi/s3md5
File details
- License:
-
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CC BYAttribution
Details
- Year of publication:
- 2020
- Verification date:
- 2020-12-17
- Dataset language:
- English
- Fields of science:
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- mathematics (Natural sciences)
- DOI:
- DOI ID 10.34808/pw16-z682 open in new tab
- Verified by:
- Gdańsk University of Technology
Keywords
References
- dataset Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 4 and homology groups with the sum of ranks less or equal to10
- dataset Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 7 and homology groups with the sum of ranks less or equal to10
- dataset Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 5 and homology groups with the sum of ranks less or equal to10
- dataset Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 6 and homology groups with the sum of ranks less or equal to10
- publication 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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