A topological introduction to define, construct and classify a class of weaves

Abstract: From innovative woven artificial muscles to garments made from traditional woven fabrics, weavings are historically well-known structures. Research on this subject is still very active in materials science, but it is very recent in mathematics. The study of weavings as new mathematical objects is very interesting in itself but also as an interdisciplinary project, with the aim of better understanding their geometric and topological structure, often associated with physical properties. This talk attempts to introduce weavings from a point of view of low dimensional topology. First, a formal definition of Euclidean and hyperbolic weavings will be stated, as well as a construction method based on the transformation of periodic uniform tilings. Next, an idea of classification for alternating structures will be discussed, extending some classical results of knot theory such as the bracket polynomial and Tait's conjectures.

computational geometryalgebraic topologycombinatoricsgeometric topologyprobability

Audience: advanced learners

Asia Pacific Seminar on Applied Topology and Geometry