Branched immersions and braids
- 36 Downloads
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.
KeywordsSurfaces in 4-manifolds Branch points Characteristic numbers Braids Transverse knots Twistors Minimal surfaces
Mathematics Subject Classification (2000)53C42
Unable to display preview. Download preview PDF.
- 1.Bennequin D.: Entrelacements et équations de Pfaff, Third Schnepfenried Geometry Conference, vol. 1 (Schnepfenried 1982), 87–161, Astérisque 107–108, Soc. Math. France, Paris (1983)Google Scholar
- 9.Ville, M.: On the normal bundle of minimal surfaces in almost Kähler manifolds. In: Anand C.K., Baird P., Loubeau E., Wood J.C. (eds.) Harmonic morphisms, harmonic maps and related topics. Pitman Res. Notes in Maths, Brest 1997 (1999)Google Scholar