4 citations · 7 across the 11 of their papers we have counts for
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The Lagrangian flux-monodromy morphism
Joé Brendel, Jean-Philippe Chassé, Rémi Leclercq
We define a new morphism on the fundamental group of the space of Lagrangian submanifolds, which takes into account the Lagrangian flux and monodromy. We study the discreteness of…
The spread construction and non-uniqueness of visible Lagrangians
Joé Brendel, Reto Kaufmann
Every even symplectic Hirzebruch surface contains a Lagrangian torus and every odd symplectic Hirzebruch surface contains a Lagrangian Klein bottle as their respective real locus.…
On Lagrangians of Oakley-Usher type
Joé Brendel, Andrea Piccirilli
The first main theme of this paper is to study symplectic (un-)knottedness of Lagrangian submanifolds which are not tori. Our construction of such Lagrangians is inspired by the ge…
A note on the cardinality of Lagrangian packings
Joé Brendel, Jean-Philippe Chassé, Laurent Côté
Given a symplectic manifold, can one pack uncountably many Lagrangian submanifolds in a given Hamiltonian isotopy class of this symplectic manifold? We address and …
Markov staircases
Nikolas Adaloglou, Joé Brendel, Jonny Evans +2
Rational homology ellipsoids are certain Liouville domains diffeomorphic to rational homology balls and having Lagrangian pin-wheels as their skeleta. From the point of view of alm…
Lagrangian split tori in and billiards
Joé Brendel, Joontae Kim
In this paper, we classify up to Hamiltonian isotopy Lagrangian tori that split as a product of circles in , when the latter is equipped with a non-monotone split s…
Semi-Local Exotic Lagrangian Tori in Dimension Four
Joé Brendel, Johannes Hauber, Joel Schmitz
We study exotic Lagrangian tori in dimension four. In certain Stein domains (which naturally appear in almost toric fibrations) we find families of monotone Lagrang…
Local exotic tori
Joé Brendel
For a broad class of symplectic manifolds of dimension at least six, we find the following new phenomenon: there exist local exotic Lagrangian tori. More specifically, let be a…
Hamiltonian Classification of toric fibres and symmetric probes
Joé Brendel
In a toric symplectic manifold, regular fibres of the moment map are Lagrangian tori which are called toric fibres. We discuss the question which two toric fibres are equivalent up…
Pinwheels as Lagrangian barriers
Joé Brendel, Felix Schlenk
The complex projective plane CP^2 contains certain Lagrangian CW-complexes called pinwheels, which have interesting rigidity properties related to solutions of the Markov equation.…
Real Lagrangian Tori and Versal Deformations
Joé Brendel
Can a given Lagrangian submanifold be realized as the fixed point set of an anti-symplectic involution? If so, it is called \emph{real}. We give an obstruction for a closed Lagrang…
On the topology of real Lagrangians in toric symplectic manifolds
Joé Brendel, Joontae Kim, Jiyeon Moon
We explore the topology of real Lagrangian submanifolds in a toric symplectic manifold which come from involutive symmetries on its moment polytope. We establish a real analog of t…