000129677 001__ 129677 000129677 005__ 20240731103352.0 000129677 0247_ $$2doi$$a10.1145/3614408.3614414 000129677 0248_ $$2sideral$$a134467 000129677 037__ $$aART-2023-134467 000129677 041__ $$aeng 000129677 100__ $$0(orcid)0000-0002-6750-8971$$aMarco-Buzunáriz, Miguel A.$$uUniversidad de Zaragoza 000129677 245__ $$aEffective homology of universal covers 000129677 260__ $$c2023 000129677 5060_ $$aAccess copy available to the general public$$fUnrestricted 000129677 5203_ $$aWe 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. 000129677 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033 000129677 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc$$uhttp://creativecommons.org/licenses/by-nc/3.0/es/ 000129677 592__ $$a0.336$$b2023 000129677 593__ $$aComputational Theory and Mathematics$$c2023$$dQ3 000129677 593__ $$aComputational Mathematics$$c2023$$dQ3 000129677 594__ $$a0.7$$b2023 000129677 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000129677 700__ $$aRomero, Ana 000129677 700__ $$aDivasón, Jose 000129677 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000129677 773__ $$g57, 2 (2023), 47-50$$pACM commun. computer algebr.$$tACM communications in computer algebra$$x1932-2232 000129677 8564_ $$s591596$$uhttps://zaguan.unizar.es/record/129677/files/texto_completo.pdf$$yVersión publicada 000129677 8564_ $$s2000088$$uhttps://zaguan.unizar.es/record/129677/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000129677 909CO $$ooai:zaguan.unizar.es:129677$$particulos$$pdriver 000129677 951__ $$a2024-07-31-09:54:46 000129677 980__ $$aARTICLE