7 papers
Non-orientable Nurikabe
Joseph Breen, Emma Copeland
We study Nurikabe puzzles on non-orientable surfaces. Specifically, we propose two versions of non-orientable Nurikabe and investigate their combinatorics on Möbius strips, Klein…
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…
Lagrangian slice disks with symplectomorphic exteriors
Joseph Breen
By modifying a construction of Abe and Tange, we exhibit arbitrarily large families of Lagrangian slice disks with Weinstein deformation equivalent exteriors. This answers a Lagran…
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…