Geometriae Dedicata

, Volume 140, Issue 1, pp 145–162 | Cite as

Branched immersions and braids

  • Marina VilleEmail author
Original Paper


Branch points of a real 2-surface Σ in a 4-manifold M generalize branch points of complex curves in complex surfaces: for example, they can occur as singularities of minimal surfaces. We investigate such a branch point p when Σ is topologically embedded. It defines a link L(p), the components of which are closed braids with the same axis up to orientation. If Σ is closed without boundary, the contribution of p to the degree of the normal bundle of Σ in M can be computed on the link L(p), in terms of the algebraic crossing numbers of its components and of their linking numbers with one another.


Surfaces in 4-manifolds Branch points Characteristic numbers Braids Transverse knots Twistors Minimal surfaces 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Institut de mathématiques de Jussieu, CNRS UMR 7586, Université Paris Diderot–Paris 7Paris Cedex 13France

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