Seifert Surfaces with Minimal Genus

Mereke van Garderen and Jarke J. van Wijk
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 453–456 Short Papers


Seifert surfaces are orientable surfaces, bounded by a mathematical knot. These surfaces have an intriguing shape and can be used to produce fascinating images and sculptures. Van Wijk and Cohen have introduced a method to generate images of these surfaces, based on braids, but their approach often led to surfaces that were too complex, i.e., the genus of the surface was too high. Here we show how minimal genus Seifert surfaces can be produced, using an extension of standard braids and an algorithm to find such surfaces.