24 citations · 41 across the 7 of their papers we have counts for
9 papers
The contact cut graph and a Weinstein -invariant
Nickolas Castro, Gabriel Islambouli, Jie Min +3
We define and study the contact cut graph which is an analogue of Hatcher and Thurston's cut graph for contact geometry, inspired by contact Heegaard splittings. We show how orient…
Relative Group Trisections
Nickolas Andres Castro, Jason Joseph, Patrick K. McFaddin
Trisections of closed 4-manifolds, first defined and studied by Gay and Kirby, have proved to be a useful tool in the systematic analysis of 4-manifolds via handlebodies. Subsequen…
Slice obstructions from genus bounds in definite 4-manifolds
Paolo Aceto, Nickolas A. Castro, Maggie Miller +2
We discuss an obstruction to a knot being smoothly slice that comes from minimum-genus bounds on smoothly embedded surfaces in definite 4-manifolds. As an example, we provide an al…
The relative -invariant of a compact -manifold
Nickolas A. Castro, Gabriel Islambouli, Maggie Miller +1
In this paper, we introduce the relative -invariant of a smooth, orientable, compact 4-manifold with boundary. This invariant is defined by measu…
On Dividing a Rectangle
Robert Dumitru, Quinn Perian, Alexander Nealey +7
This paper deals with the history of the following problem: "Can an arbitrary rectangle be dissected into 3 non-rectangular congruent regions?" We present a new elementary proof th…
Trisections of 4-manifolds with Boundary
Nickolas A. Castro, David T. Gay, Juanita Pinzón-Caicedo
Given a handle decomposition of a 4-manifold with boundary, and an open book decomposition of the boundary, we show how to produce a trisection diagram of a trisection of the 4-man…