Knot theory and entanglement in biopolymers - Barbensi, A (2020)
This thesis is divided into two parts, each summarising one of the main projects I have undertaken since the beginning of my DPhil. In the first project, we study the graph associated to a knot K, whose vertices are diagrams representing K, and edges represent single Reidemeister moves. We prove that the isomorphism type of this graph is a complete knot invariant, up to mirroring. This framework suggests a discretised model to study the action of some enzymes on knotted DNA molecules. More specifically, we use a grid diagrams based model to investigate the topological consequences of intersegmental passages occurring in circular DNA molecules. We suggest a grid diagrams-based calculation as a new and computationally convenient framework for investigating knotting probabilities in biopolymers.