Banchoff’s sphere and branched covers over the trefoil

Lozano Rojo, Á. ; Vigara, R.

Resumen: A 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.

Idioma: Inglés

DOI: 10.1007/s13398-017-0477-5

Año: 2018

Publicado en: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 112, 3 (2018), 751-765
ISSN: 1578-7303

Factor impacto JCR: 1.028 (2018)

Categ. JCR: MATHEMATICS rank: 87 / 313 = 0.278 (2018) - Q2 - T1

Factor impacto SCIMAGO: 0.565 - Algebra and Number Theory (Q2) - Analysis (Q2) - Geometry and Topology (Q2) - Computational Mathematics (Q2) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E15
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2013-45710-C2
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2013-46337-C2-2
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2016-76868-C2-2-P
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77642-C2

Tipo y forma: Article (PostPrint)