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manuscripta mathematica

, Volume 100, Issue 4, pp 405–422 | Cite as

Stiefel–Whitney surfaces and the tri-genus of non-orientable 3-manifolds

  • Wolfgang Heil
  • Víctor Núñez
  • J. C. Gómez-Larrañaga
  • 32 Downloads

Abstract:

Every non-orientable 3-manifold M can be expressed as a union of three orientable handlebodies V 1,V 2,V 3 whose interiors are pairwise disjoint. If g i denotes the genus of ∂V i and g 3g 2g 3, then the tri-genus of M is the minimum triple (g 1,g 2,g 3), ordered lexicographically. If the Bockstein of the first Stiefel–Whitney class βw 1(M)=0, then M has tri-genus (0,2g,g 3), where g is the minimal genus of a 2-sided Stiefel Whitney surface of M. In this paper it is shown that, if βw 1(M)&\ne;0, then M has tri-genus (1,2g−1,g 3), where g is the minimal genus of a (1-sided) Stiefel–Whitney surface. As an application the tri-genus of certain graph manifolds is computed.

Mathematics Subject Classification (1991):57N10, 57M50 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Wolfgang Heil
    • 1
  • Víctor Núñez
    • 1
  • J. C. Gómez-Larrañaga
    • 2
  1. 1.Department of Mathematics, Florida State University, Tallahasee, FL 32312, USA. E-mail: heil@math.fsu.eduUS
  2. 2.Centro de Investigación en Matemáticas, A. P. 402, Guanajuato 36000, Gto. MéxicoMX

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