Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Islambouli, Gabriel"'
Autor:
Castro, Nickolas, Islambouli, Gabriel, Min, Jie, Sakallı, Sümeyra, Starkston, Laura, Wu, Angela
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 oriented paths in the contact cut graph correspond to Lefschetz fibrations a
Externí odkaz:
http://arxiv.org/abs/2408.05340
Autor:
Islambouli, Gabriel, Starkston, Laura
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
Externí odkaz:
http://arxiv.org/abs/2303.00906
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
Externí odkaz:
http://arxiv.org/abs/2206.04161
Autor:
Islambouli, Gabriel
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 paper, we prove a corr
Externí odkaz:
http://arxiv.org/abs/2111.08924
Autor:
Islambouli, Gabriel, Naylor, Patrick
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 sh
Externí odkaz:
http://arxiv.org/abs/2010.03057
Autor:
Islambouli, Gabriel, Klug, Michael
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
Externí odkaz:
http://arxiv.org/abs/1912.02325
Publikováno v:
Pacific J. Math. 315 (2021) 305-346
In this paper, we introduce the relative $\mathcal{L}$-invariant $r\mathcal{L}(X)$ 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 s
Externí odkaz:
http://arxiv.org/abs/1908.05371
Autor:
Islambouli, Gabriel
The goal of this paper is to construct distinct trisections of the same genus on a fixed 4-manifold. For every $k \geq 2$, we construct $2^{k}-1$ non-diffeomorphic $(3k,k)$-trisections on infinitely many 4-manifolds. Here, the manifolds are spun Seif
Externí odkaz:
http://arxiv.org/abs/1804.06978
Autor:
Islambouli, Gabriel
Publikováno v:
Algebr. Geom. Topol. 18 (2018) 1799-1822
Given two smooth, oriented, closed 4-manifolds $M_1$ and $M_2$, we construct two invariants, $D^P(M_1, M_2)$ and $D(M_1, M_2)$, coming from distances in the pants complex and the dual curve complex respectively. To do this, we adapt work of Johnson o
Externí odkaz:
http://arxiv.org/abs/1707.07108
Autor:
Islambouli, Gabriel, Willis, Michael
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 Jones-Wenzl projectors using the limiting complex of infinite torus bra
Externí odkaz:
http://arxiv.org/abs/1610.04582