38 citations · 176 across the 20 of their papers we have counts for
21 papers
Floer Homology with DG Coefficients. Applications to cotangent bundles
Jean-François Barraud, Mihai Damian, Vincent Humilière +1
We define Hamiltonian Floer homology with differential graded (DG) local coefficients for symplectically aspherical manifolds. The differential of the underlying complex involves c…
Higher Dimensional Birkhoff attractors (with an appendix by Maxime Zavidovique)
Marie-Claude Arnaud, Vincent Humilière, Claude Viterbo
We extend to higher dimensions the notion of Birkhoff attractor of a dissipative map. We prove that this notion coincides with the classical Birkhoff attractor. We prove that for t…
Essential loops in completions of Hamiltonian groups
Vincent Humilière, Alexandre Jannaud, Rémi Leclercq
We initiate the study of the fundamental group of natural completions of the group of Hamiltonian diffeomorphisms, namely its -closure and its c…
Morse homology with DG coefficients
Jean-François Barraud, Mihai Damian, Vincent Humilière +1
We develop a theory of Morse homology and cohomology with coefficients in a derived local system, for manifolds and also more generally for colimits of spaces that have the homotop…
The -support as a micro-support
Tomohiro Asano, Stéphane Guillermou, Vincent Humilière +2
We prove that for any element in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the -…
Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces
Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak +2
This paper continues the study of link spectral invariants on compact surfaces, introduced in our previous work and shown to satisfy a Weyl law in which they asymptotically recover…
Quantitative Heegaard Floer cohomology and the Calabi invariant
Daniel Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak +2
We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi…
PFH spectral invariants on the two-sphere and the large scale geometry of Hofer's metric
Dan Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini
We resolve three longstanding questions related to the large scale geometry of the group of Hamiltonian diffeomorphisms of the two-sphere, equipped with Hofer's metric. Namely: (1)…
Proof of the simplicity conjecture
Dan Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving homeomorphisms of the -ball is simple for , asked if the same statement holds…
An Arnold-type principle for non-smooth objects
Lev Buhovsky, Vincent Humilière, Sobhan Seyfaddini
In this article we study the Arnold conjecture in settings where objects under consideration are no longer smooth but only continuous. The example of a Hamiltonian homeomorphism, o…
The action spectrum and C^0 symplectic topology
Lev Buhovsky, Vincent Humilière, Sobhan Seyfaddini
Our first main result states that the spectral norm on the group of Hamiltonian diffeomorphisms, introduced in the works of Viterbo, Schwarz and Oh, is continuous with respect to t…
A C^0 counterexample to the Arnold conjecture
Lev Buhovsky, Vincent Humilière, Sobhan Seyfaddini
The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold must have at least as many fixed points as the minimal number of critic…
Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces
Vincent Humilière, Frédéric Le Roux, Sobhan Seyfaddini
Inspired by Le Calvez' theory of transverse foliations for dynamical systems of surfaces, we introduce a dynamical invariant, denoted by N, for Hamiltonians of any surface other th…
Reduction of symplectic homeomorphisms
Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini
In a previous article, we proved that symplectic homeomorphisms preserving a coisotropic submanifold C, preserve its characteristic foliation as well. As a consequence, such symple…
Coisotropic rigidity and C^0-symplectic geometry
Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini
We prove that symplectic homeomorphisms, in the sense of the celebrated Gromov-Eliashberg Theorem, preserve coisotropic submanifolds and their characteristic foliations. This resul…
New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians
Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini
We prove a new variant of the energy-capacity inequality for closed rational symplectic manifolds (as well as certain open manifolds such as cotangent bundle of closed manifolds...…
Hofer's distance on diameters and the Maslov index
Vincent Humiliere
We prove that Hofer's distance between two diameters of the open 2-disk admits an upper bound in terms of the Maslov index of their intersection points.
On the geometry of the space of fibrations
Vincent Humiliere, Nicolas Roy
We study geometrical aspects of the space of fibrations between two given manifolds M and B, from the point of view of Frechet geometry. As a first result, we show that any connect…
The Calabi invariant for some groups of homeomorphisms
Vincent Humiliere
We show that the Calabi homomorphism extends to some groups of homeomorphisms on exact symplectic manifolds. The construction is based on the uniqueness of the generating Hamiltoni…
Hamiltonian pseudo-representations
Vincent Humilière
The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a nor…
On some completions of the space of Hamiltonian maps
Vincent Humilière
We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their…