Gabriel Islambouli

The contact cut graph and a Weinstein L$\mathcal {L}$‐invariant

Nickolas A. Castro, Gabriel Islambouli, Jie Min, Sümeyra Sakallı et autres

Abstract 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 (Giroux, Proceedings of the International Congress of Mathematicians , Beijing, 2002; Torisu, Internat. Math. Res. …

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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 the pants complex, or as a multisection. In this …

Multisections with divides and Weinstein 4-manifolds

Gabriel Islambouli, Laura Starkston

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Toric multisections and curves in rational surfaces

Gabriel Islambouli, Homayun Karimi, Peter Lambert‐Cole, Jeffrey Meier

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 smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth …

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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 curves. We give two algorithms to construct a multisection diagram with divides …

Toric multisections and curves in rational surfaces

Gabriel Islambouli, Homayun Karimi, Peter Lambert‐Cole, Jeffery L. Meier

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 if it admits an effective torus action. Orlik and Raymond showed that these 4-manifolds are precisely …

The relative ℒ-invariant of a compact 4-manifold

Nickolas A. Castro, Gabriel Islambouli, Maggie Miller, Maggy Tomova

In this paper, we introduce the relative L-invariant rL(X) of a smooth, orientable, compact 4-manifold X with boundary.This invariant is defined by measuring the lengths of certain paths in the cut complex of a trisection surface for X.This is motivated by the …

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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 the pants complex, or as a multisection. In this …

Nielsen equivalence and trisections

Gabriel Islambouli

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Representing smooth $4$-manifolds as loops in the pants complex

Gabriel Islambouli, Michael R. 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 pants complex is simply connected, to provide an elementary proof that such 4-manifolds …

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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 smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth …