Dressing preserving the fundamental group

Abstract

In this note we consider the relationship between the dressing action and the holonomy representation in the context of constant mean curvature surfaces. We characterize dressing elements that preserve the topology of a surface and discuss dressing by simple factors as a means of adding bubbles to a class of non finite type cylinders.

36 pages, 1 figure

References in corpus (4)

• Isothermic surfaces: conformal geometry, Clifford algebras and integrable systems
• On symmetries of constant mean curvature surfaces
• Constant Mean Curvature Trinoids
• Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions

Cited by in corpus (5)

• Darboux transforms and simple factor dressing of constant mean curvature surfaces
• Loop Group Methods for Constant Mean Curvature Surfaces
• Harmonic maps, Backlund-Darboux transformations and "line soliton" analogs
• Discrete constant mean curvature surfaces via conserved quantities
• Simple factor dressing and the Lopez-Ros deformation of minimal surfaces in Euclidean 3-space