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Genera of coverings of torus bundles

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

After showing that a covering space of surface bundles over \(S^1\) factors as a ‘covering of fibers’ followed by a ‘power covering’, we prove that, for torus bundles, there are fiber coverings that lower the genus only for bundles that are double branched coverings of the 3-sphere, and for the same family, bundles that double cover \(S^3\), we show that power coverings do not lower Heegaard genus.

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Authors and Affiliations

  1. CIMAT, A.P. 402, 36000, Guanajuato, GTO, Mexico

    Víctor Núñez & Enrique Ramírez-Losada

  2. DACB, Universidad Juárez Autónoma de Tabasco, Km. 1 Carr. Cunduacán-Jalpa de Méndez, 86690, Cunduacán, TAB, Mexico

    Jair Remigio-Juárez

Authors
  1. Víctor Núñez
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  2. Enrique Ramírez-Losada
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  3. Jair Remigio-Juárez
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Corresponding author

Correspondence to Víctor Núñez.

Additional information

To Professor María Teresa Lozano on the occasion of her 70th birthday.

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Núñez, V., Ramírez-Losada, E. & Remigio-Juárez, J. Genera of coverings of torus bundles. RACSAM 112, 811–827 (2018). https://doi.org/10.1007/s13398-017-0483-7

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  • DOI: https://doi.org/10.1007/s13398-017-0483-7

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