Immersed flat ribbon knots
Thursday, June 27, 2019 - 10:15am - 11:15am
The ribbonlength problem aims to find the minimal ratio between the length of the core to the ribbon width over all the planar realisations in a knot or link type. We present a method for studying the ribbonlength problem for immersed planar ribbon knots and links. This is achieved by embedding the space of immersed planar ribbon knots and links into a larger space of disk diagrams by imposing some natural geometric restrictions on the allowable immersions. When length minimisers in the space of disk diagrams are ribbon, then these solve the ribbonlength problem. We also provide examples when minimisers in the space of disk diagrams are not ribbon and state some conjectures. We compute the minimal ribbonlength of some small knot and link diagrams and certain infinite families of link diagrams.