Effective Homology of Universal Covers-Reference-Cited by-同舟云学术

Effective Homology of Universal Covers

Published:2023-06 Issue:2 Volume:57 Page:47-50
ISSN:1932-2240
Container-title:ACM Communications in Computer Algebra
language:en
Short-container-title:ACM Commun. Comput. Algebra

Author:

Marco-Buzunáriz Miguel A.¹,Romero Ana²,Divasón Jose²

Affiliation:

1. University of Zaragoza, Spain

2. University of La Rioja, Spain

Abstract

We present an algorithm for constructing the effective homology for the universal cover of simplicial sets with effective homology, provided that a nilpotency condition holds. This can be useful for computing higher homotopy groups, since this process can be seen as the first step in the Whitehead tower. Our algorithm can be applied to some spaces satisfying a particular condition. We also present implementations of this method in SageMath and Kenzo.

Publisher

Association for Computing Machinery (ACM)

Subject

Microbiology (medical),Immunology,Immunology and Allergy

Link

https://dl.acm.org/doi/pdf/10.1145/3614408.3614414

Reference6 articles.

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2. X. Dousson J. Rubio F. Sergeraert and Y. Siret. The Kenzo program. http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/ 1999. X. Dousson J. Rubio F. Sergeraert and Y. Siret. The Kenzo program. http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/ 1999.

3. M. A. Marco-Buzunáriz , J. Divasón , and A. Romero . Universal covers in Kenzo. https://github.com/ana-romero/Kenzo-external-modules , 2023 . M. A. Marco-Buzunáriz, J. Divasón, and A. Romero. Universal covers in Kenzo. https://github.com/ana-romero/Kenzo-external-modules, 2023.

4. The Computability Problem in Algebraic Topology

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