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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 4 and homology groups with the sum of ranks less or equal to10
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 4 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 4 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:
-
- mathematics (Natural sciences)
- DOI:
- DOI ID 10.34808/8wws-td98 open in new tab
- Funding:
- 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 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
- 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
- publication Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
- 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 8 and homology groups with the sum of ranks less or equal to 10
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