Penn Arts & Sciences Logo

Graduate Student Geometry-Topology Seminar

Wednesday, April 19, 2023 - 12:00pm

Sonia Mahmoudi

UPenn (physics)


University of Pennsylvania


Topological weaves are complex entangled structures defined as an embedding of infinitely many simple open curves in the thickened plan. In the case of a doubly periodic structure, the topology is entirely encoded in any generating cell of the infinite diagram, which is a particular link diagram on a torus. However, when studying equivalence classes of doubly periodic weaves, one must consider the infinite number of possibilities to choose a generating cell, namely all the links that lift to equivalent weaves in the universal cover. In this talk, we will introduce a new weaving invariant that describes entanglement on a torus diagram to classify doubly periodic (p,q)-weaves. This is a joint work with Prof. Motoko Kotani and Dr. Mizuki Fukuda.