The Triple-Point Spectrum of Closed Orientable 3-Manifolds

  • Álvaro Lozano RojoEmail author
  • Rubén Vigara


The triple-point numbers and the triple-point spectrum of a closed 3-manifold are topological invariants that give a measure of the complexity of the 3-manifold using the number of triple points of minimal filling Dehn surfaces. Basic properties of these invariants are presented, and the triple-point spectra of \(\mathbb {S}^2\times \mathbb {S}^1\) and \(\mathbb {S}^3\) are computed.


3-Manifold homology 3-sphere immersed surface filling Dehn surface triple points complexity of 3-manifolds 

Mathematics Subject Classification

Primary 57N10 57N35 57M27 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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