Publications (12)
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…
The Giroux correspondence in arbitrary dimensions
Joseph Breen, Ko Honda, Yang Huang
We establish the Giroux correspondence in arbitrary dimensions. As corollaries we (i) give an alternate proof of a result of Giroux-Pardon that states that any Weinstein domain is…
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…
Regularly slice implies once-stably decomposably slice
Joseph Breen
We investigate the relationship between regular and decomposable Lagrangian cobordisms in -dimensional symplectizations. First, we show that regular sliceness implies once-stabl…
Regular Lagrangians in Lefschetz fibrations
Joseph Breen, Agniva Roy, Luya Wang
We characterize regularity of Lagrangian submanifolds in Weinstein Lefschetz fibrations, establishing a conjecture of Giroux and Pardon. Our main result is the Weinstein analogue o…
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…