10 citations · 15 across the 9 of their papers we have counts for
10 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…
Multisections with divides and Weinstein 4-manifolds
Gabriel Islambouli, Laura Starkston
We show how to encode a Weinstein 4-manifold using a multisection diagram with divides, which is a sequence of cut systems on a surface, together with a separating collection of cu…
Toric multisections and curves in rational surfaces
Gabriel Islambouli, Homayun Karimi, Peter Lambert-Cole +1
We study multisections of embedded surfaces in 4-manifolds admitting effective torus actions. We show that a simply-connected 4-manifold admits a genus one multisection if and only…
Uniqueness of 4-manifolds described as sequences of 3-d handlebodies
Gabriel Islambouli
Work of numerous authors has shown that any smooth, orientable, closed 4-manifold may be described as a loop of Morse functions on a surface, a loop in the cut complex, a loop in t…
Multisections of 4-manifolds
Gabriel Islambouli, Patrick Naylor
We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smoo…
Representing smooth 4-manifolds as loops in the pants complex
Gabriel Islambouli, Michael Klug
We show that every smooth, orientable, closed, connected 4-manifold can be represented by a loop in the pants complex. We use this representation, together with the fact that the p…
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…
Nielsen equivalence and trisections of 4-manifolds
Gabriel Islambouli
The goal of this paper is to construct distinct trisections of the same genus on a fixed 4-manifold. For every , we construct non-diffeomorphic -trisect…
Comparing 4-Manifolds in the Pants Complex via Trisections
Gabriel Islambouli
Given two smooth, oriented, closed 4-manifolds and , we construct two invariants, and , coming from distances in the pants complex and the d…
The Khovanov homology of infinite braids
Gabriel Islambouli, Michael Willis
We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the J…