2 citations · 2 across the 8 of their papers we have counts for
10 papers
Derivative links in contact topology
Joseph Breen, Alexander Zupan
We import the theory of -links and derivative links into contact topology in both the Legendrian and transverse setting. This framework is used to characterize various forms of…
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…
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…
Quasipositive fiber surfaces are not well-quasi-ordered
Joseph Breen, Michele Capovilla-Searle
By exhibiting an explicit infinite anti-chain, we show that the class of quasipositive fiber surfaces in is not well-quasi-ordered under the surface minor relation. This answ…
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 b…
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…
Folded symplectic forms in contact topology
Joseph Breen
We establish the relationship between folded symplectic forms and convex hypersurface theory in contact topology. As an application, we use convex hypersurface theory to reprove an…
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…
Morse-Smale characteristic foliations and convexity in contact manifolds
Joseph Breen
We generalize a result of Giroux which says that a closed surface in a contact -manifold with Morse-Smale characteristic foliation is convex. Specifically, we show that the resu…