5 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…
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…
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…