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Branched immersions and braids

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Abstract

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.

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  1. Institut de mathématiques de Jussieu, CNRS UMR 7586, Université Paris Diderot–Paris 7, Site Chevaleret, Case 7012, 75205, Paris Cedex 13, France

    Marina Ville

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  1. Marina Ville
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Correspondence to Marina Ville.

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Ville, M. Branched immersions and braids. Geom Dedicata 140, 145–162 (2009). https://doi.org/10.1007/s10711-008-9313-6

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  • DOI: https://doi.org/10.1007/s10711-008-9313-6

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