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On the subadditivity of Montesinos complexity of closed orientable 3-manifolds

  • Álvaro Lozano
  • Rubén Vigara
Original Paper

Abstract

A filling Dehn sphere \(\varSigma \) in a closed 3-manifold \(M\) is a sphere transversely immersed in \(M\) that defines a cell decomposition of \(M\). Every closed 3-manifold has a filling Dehn sphere Montesinos-Amilibia (Contribuciones Matemáticas: Homenaje a Joaquín Arregui Fernández, Editorial Complutense, pp 239–247, 2000). The Montesinos complexity of a \(3\)-manifold \(M\) is defined as the minimal number of triple points among all the filling Dehn spheres of \(M\). A sharp upper bound for the Montesinos complexity of the connected sum of two 3-manifolds is given.

Keywords

3-Manifold Immersed surface Filling Dehn sphere Triple points Complexity of 3-manifolds 

Mathematics Subject Classification (2010)

57N10 57N35 

Notes

Acknowledgments

The authors sincerely thank to the referees for their valuable comments and suggestions. We also thank Prof. J.M. Montesinos for his advices about the content of this paper.

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Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  1. 1.Centro Universitario de la Defensa ZaragozaZaragozaSpain
  2. 2.IUMA, Universidad de ZaragozaZaragozaSpain

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