2 citations · 6 across the 9 of their papers we have counts for
9 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…
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…
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…
Persistent Legendrian contact homology in
Maya Basu, Austin Christian, Ethan Clayton +3
This work applies the ideas of persistent homology to the problem of distinguishing Legendrian knots. We develop a persistent version of Legendrian contact homology by filtering th…
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…
Some applications of Menke's JSJ decomposition for symplectic fillings
Austin Christian, Youlin Li
We apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserv…
On symplectic fillings of virtually overtwisted torus bundles
Austin Christian
We use Menke's JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted torus bundles to…
Splitting symplectic fillings
Austin Christian, Michael Menke
We generalize the mixed tori which appear in the second author's JSJ-type decomposition theorem for symplectic fillings of contact manifolds. Mixed tori are convex surfaces in cont…
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…