Saul Schleimer and Henry Segerman

Reader (SS), Assistant Professor (HS)
Mathematics Institute, University of Warwick (SS), Department of Mathematics, Oklahoma State University (HS)
Coventry, United Kingdom (SS), Stillwater, Oklahoma (HS)
Saul Schleimer is a geometric topologist, working at the University of Warwick. His other interests include combinatorial group theory and computation. He is especially interested in the interplay between these fields and additionally in visualization of ideas from these fields.

Henry Segerman is an assistant professor in the department of mathematics at Oklahoma State University. His research interests are in three-dimensional geometry and topology, and in mathematical art and visualization. In visualization, he works mostly in the medium of 3D printing, with other interests in spherical video, virtual, and augmented reality. He is the author of the book "Visualizing Mathematics with 3D Printing".
Trefoil spine
9 x 9 x 8 cm
3D printed nylon plastic
2015
A spine of a three-dimensional manifold with boundary is a two-dimensional complex that the manifold deformation retracts to. Here, we show the trefoil knot, together with a spine of its complement in the three-sphere, stereographically projected to euclidean space.

The windows form a distorted rectangular grid, with all angles 90 degrees. In one grid direction the windows lie along semicircles, each with both ends on the vertical axis. In the other grid direction, the windows trace out trefoil knots. The only exception is the windows meeting the dual circle to the vertical axis.

This design was suggested to us by Dylan Thurston.