000079154 001__ 79154 000079154 005__ 20200117221641.0 000079154 0247_ $$2doi$$a10.1007/s13398-017-0477-5 000079154 0248_ $$2sideral$$a107089 000079154 037__ $$aART-2018-107089 000079154 041__ $$aeng 000079154 100__ $$0(orcid)0000-0002-1184-5901$$aLozano Rojo, Á. 000079154 245__ $$aBanchoff’s sphere and branched covers over the trefoil 000079154 260__ $$c2018 000079154 5060_ $$aAccess copy available to the general public$$fUnrestricted 000079154 5203_ $$aA filling Dehn surface in a 3-manifold M is a generically immersed surface in M that induces a cellular decomposition of M. Given a tame link L in M, there is a filling Dehn sphere of M that “trivializes” (diametrically splits) it. This allows to construct filling Dehn surfaces in the coverings of M branched over L. It is shown that one of the simplest filling Dehn spheres of S3 (Banchoff’s sphere) diametrically splits the trefoil knot. Filling Dehn spheres, and their Johansson diagrams, are constructed for the coverings of S3 branched over the trefoil. The construction is explained in detail. Johansson diagrams for generic cyclic coverings and for the simplest locally cyclic and irregular ones are constructed explicitly, providing new proofs of known results about cyclic coverings and the 3-fold irregular covering over the trefoil. 000079154 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E15$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2013-45710-C2$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2013-46337-C2-2$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-76868-C2-2-P$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77642-C2 000079154 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000079154 590__ $$a1.028$$b2018 000079154 591__ $$aMATHEMATICS$$b87 / 313 = 0.278$$c2018$$dQ2$$eT1 000079154 592__ $$a0.565$$b2018 000079154 593__ $$aAlgebra and Number Theory$$c2018$$dQ2 000079154 593__ $$aAnalysis$$c2018$$dQ2 000079154 593__ $$aGeometry and Topology$$c2018$$dQ2 000079154 593__ $$aComputational Mathematics$$c2018$$dQ2 000079154 593__ $$aApplied Mathematics$$c2018$$dQ2 000079154 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000079154 700__ $$0(orcid)0000-0001-7111-5022$$aVigara, R. 000079154 773__ $$g112, 3 (2018), 751-765$$pRev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.$$tRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas$$x1578-7303 000079154 8564_ $$s934720$$uhttps://zaguan.unizar.es/record/79154/files/texto_completo.pdf$$yPostprint 000079154 8564_ $$s9776$$uhttps://zaguan.unizar.es/record/79154/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000079154 909CO $$ooai:zaguan.unizar.es:79154$$particulos$$pdriver 000079154 951__ $$a2020-01-17-22:04:24 000079154 980__ $$aARTICLE