Algebra Seminar: Dancso -- Crossing-less knot diagrams on 3-manifold spines

Zsuzsanna Dancso (University of Sydney) 

Friday 1 April, 12-1pm, Place: Carslaw 273 

Title: Crossing-less knot diagrams on 3-manifold spines 

Abstract: 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.