The database of odd algebraic periods for quasi-unipotent self-maps of a space having the same homology group as the connected sum of g tori

Description

Algebraic periods defined in terms of Lefschetz numbers of iterations are an important tool for studying periodic points. A map is called quasi-unipotent if all eigenvalues of the induced maps on the homology groups with rational coefficients are roots of unity.

The dataset consists of 20 files indexed by numbers g=1,...,20. Each file provides sets of odd algebraic periods for all quasi-unipotent self-maps of a space having the same homology groups as the connected sum of g tori. Let us remark that each data set covers all algebraical restrictions that come from zeta functions for the sets of minimal Lefschetz periods of Morse–Smale diffeomorphisms of M(g) being the connected sum of g tori.

The results are based on the algorithm available in the paper: G. Graff, M. Lebiedź, A. Myszkowski, Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms, J. Fixed Point Theory Appl. (2019) 21:47, https://doi.org/10.1007/s11784-019-0680-4.

Dataset file

torus_all.zip

19.5 kB, S3 ETag a7c5c699964c3d5434fce9facccf4d82-1, downloads: 16

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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

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Details

Year of publication:

2020

Verification date:

2021-01-04

Dataset language:

English

Fields of science:

mathematics (Natural sciences)

DOI:

10.34808/faqj-rx17

Funding:

Topological invariants: the structure of a space and its self-maps

Verified by:

Gdańsk University of Technology

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