University of Sydney Algebra Seminar
Zsuzsanna Dancso (University of Sydney)
Friday 1 April, 12-1pm, Place: Carslaw 273
Crossing-less knot diagrams on 3-manifold spines
I will introduce the most unlikely theorem of the history of mathematics - not because of the content therein, but because of the way it came about. In the talk I will share the story, but for now, just the content. A "spine" is a surface (2-complex) inside a three manifold, onto which the manifold less a few points deformation retracts. In this way, spines help generalise link projections from R^3 to general 3-manifolds. We find that these link projections can always be made crossing-less, and furthermore, a set of "crossing-less moves" are sufficient to describe isotopy classes of links: a crossing-less "Reidemeister theorem" for link projections on three-manifold spines. I might mention possible implications for 4-manifolds too. Knowledge of 3- or 4-manifolds not necessary. Joint work with Jack Brand, Ben Burton, Alex He, Adele Jackson, and Joan Licata.