000151550 001__ 151550
000151550 005__ 20251017144642.0
000151550 0247_ $$2doi$$a10.1016/j.jsc.2024.102401
000151550 0248_ $$2sideral$$a140586
000151550 037__ $$aART-2024-140586
000151550 041__ $$aeng
000151550 100__ $$0(orcid)0000-0002-6750-8971$$aMarco-Buzunáriz, Miguel A.$$uUniversidad de Zaragoza
000151550 245__ $$aComputing the homology of universal covers via effective homology and discrete vector fields
000151550 260__ $$c2024
000151550 5060_ $$aAccess copy available to the general public$$fUnrestricted
000151550 5203_ $$aEffective homology techniques allow us to compute homology groups of a wide family of topological spaces. By the Whitehead tower method, this can also be used to compute higher homotopy groups. However, some of these techniques (in particular, the Whitehead tower) rely on the assumption that the starting space is simply connected. For some applications, this problem could be circumvented by replacing the space by its universal cover, which is a simply connected space that shares the higher homotopy groups of the initial space. In this paper, we formalize a simplicial construction for the universal cover, and represent it as a twisted Cartesian product.
As we show with some examples, the universal cover of a space with effective homology does not necessarily have effective homology in general. We show two independent sufficient conditions that can ensure it: one is based on a nilpotency property of the fundamental group, and the other one on discrete vector fields.
Some examples showing our implementation of these constructions in both SageMath and Kenzo are shown, together with an approach to compute the homology of the universal cover when the group is Abelian even in some cases where there is no effective homology, using the twisted homology of the space.
000151550 536__ $$9info:eu-repo/grantAgreement/ES/AEI/PID2020-116641GB-I00$$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033
000151550 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
000151550 590__ $$a1.1$$b2024
000151550 592__ $$a0.533$$b2024
000151550 591__ $$aMATHEMATICS, APPLIED$$b162 / 343 = 0.472$$c2024$$dQ2$$eT2
000151550 593__ $$aComputational Mathematics$$c2024$$dQ2
000151550 591__ $$aCOMPUTER SCIENCE, THEORY & METHODS$$b92 / 147 = 0.626$$c2024$$dQ3$$eT2
000151550 593__ $$aAlgebra and Number Theory$$c2024$$dQ2
000151550 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000151550 700__ $$aRomero, Ana
000151550 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología
000151550 773__ $$g128 (2024), 102401 [28 pp.]$$pJ. symb. comput.$$tJOURNAL OF SYMBOLIC COMPUTATION$$x0747-7171
000151550 8564_ $$s272009$$uhttps://zaguan.unizar.es/record/151550/files/texto_completo.pdf$$yVersión publicada
000151550 8564_ $$s1670878$$uhttps://zaguan.unizar.es/record/151550/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000151550 909CO $$ooai:zaguan.unizar.es:151550$$particulos$$pdriver
000151550 951__ $$a2025-10-17-14:32:45
000151550 980__ $$aARTICLE