Geometry of self-propulsion at low reynolds number

The problem of swimming at low Reynolds number is formulated in terms of a gauge field on the space of shapes. Effective methods for computing this field, by solving a linear boundary-value problem, are described. We employ conformal-mapping techniques to calculate swimming motions for cylinders with a variety of cross-sections. We also determine the net translational motion due to arbitrary infinitesimal deformations of a sphere.