# Desingularization of branch points of minimal surfaces in $\mathbb{R}^4$ (II)

Abstract : We desingularize a branch point $p$ of a minimal disk $F_0(\mathbb{D})$ in $\mathbb{R}^4$ through immersions $F_t$'s which have only transverse double points and are branched covers of the plane tangent to $F_0(\mathbb{D})$ at $p$. If $F_0$ is a topological embedding and thus defines a knot in a sphere/cylinder around the branch point, the data of the double points of the $F_t$'s give us a braid representation of this knot as a product of bands.
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Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-01135924
Contributor : Marina Ville <>
Submitted on : Thursday, March 26, 2015 - 11:17:20 AM
Last modification on : Thursday, December 5, 2019 - 1:26:34 AM

### Identifiers

• HAL Id : hal-01135924, version 1
• ARXIV : 1503.07229

### Citation

Marina Ville. Desingularization of branch points of minimal surfaces in $\mathbb{R}^4$ (II). 2015. ⟨hal-01135924⟩

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