6 papers
Hard Legendrian unknots
Joseph Breen, Austin Christian, Angela Wu
We initiate the study of Reidemeister hardness of Legendrian unknot front projections. Using normal rulings, we obstruct several infinite families of hard unknot diagrams from bein…
Convex hypersurface theory in contact topology
Joseph Breen, Austin Christian, Ko Honda +1
We lay the foundations of convex hypersurface theory in contact topology, extending the work of Giroux in dimension three. Specifically, we prove that any closed hypersurface in a…
Bypass moves in convex hypersurface theory
Joseph Breen, Austin Christian
We construct bypass attachments in higher dimensional contact manifolds that, when attached to a neighborhood of a Weinstein hypersurface, yield a neighborhood of a new Weinstein h…
Mixed tori in contact surgery diagrams
Austin Christian, Tanushree Shah
We develop a diagrammatic framework for applying the symplectic JSJ decomposition to exact/weak symplectic fillings of 3-dimensional contact manifolds. Namely, we apply the symplec…
Torus bundle Liouville domains are stably Weinstein
Joseph Breen, Austin Christian
We develop explicit local operations that may be applied to Liouville domains, with the goal of simplifying the dynamics of the Liouville vector field. These local operations, whic…
A JSJ-type decomposition theorem for symplectic fillings
Austin Christian, Michael Menke
We establish a JSJ-type decomposition theorem for splitting exact symplectic fillings of contact 3-manifolds along \emph{mixed tori} -- these are convex tori satisfying a particula…