Database of the estimations of the numbers of simplices of triangulation of some classical Lie groups - Open Research Data - Bridge of Knowledge

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Database of the estimations of the numbers of simplices of triangulation of some classical Lie groups

Description

It is know that any smooth manifold can be triangulated. The number of simplices of triangulation of a given manifold depends on its topological and combinatorial structure. The data consists of the lower bounds for the numbers of simplices of each dimension of any triangulation of classical Lie groups U(n), SU(n), Sp(n), and SO(n) for n up to 25. Each file devotes to one group, and gives one integer vector {f0, f1, ... , fd} of length d+1, where d is the dimension of the Lie group, and each fj is a lower bound for the number of simplices of dimension j. The files are in the form of plain text with filename: type of Lie group + index n + ".txt". The theoretical arguments and algorithm for computing these data are contained in the paper: Haibao Duan, Wacław Marzantowicz, Xuezhi Zhao, On the number of simplices required to triangulate a Lie group, Topology and its applications, to appear (see also arXiv:2003.13125).

Dataset file

g4.zip
1.3 MB, S3 ETag 2395e0a64b8b55fda61bde29307c5811-1, downloads: 20
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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
download file g4.zip

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License:
Creative Commons: by 4.0 open in new tab
CC BY
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Details

Year of publication:
2020
Verification date:
2020-12-17
Dataset language:
English
Fields of science:
  • mathematics (Natural sciences)
DOI:
DOI ID 10.34808/14t7-n323 open in new tab
Funding:
Verified by:
Gdańsk University of Technology

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