Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Humilière, Vincent"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G8, Pp 1333-1340 (2023)
We prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma $-support of $L$ coincides with the reduced micro-support of its s
Externí odkaz:
https://doaj.org/article/0b2ead7c739f43e0aec9b182048d1ca3
We define Hamiltonian Floer homology with differential graded (DG) local coefficients for symplectically aspherical manifolds. The differential of the underlying complex involves chain representatives of the fundamental classes of the moduli spaces o
Externí odkaz:
http://arxiv.org/abs/2404.07953
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 the dissipative system associated to the discounted Hamilton-Jacobi equ
Externí odkaz:
http://arxiv.org/abs/2404.00804
We initiate the study of the fundamental group of the group of Hamiltonian homeomorphisms denoted by $\overline{\mathrm{Ham}}(M,\omega)$, i.e. the $C^0$-closure of the group of Hamiltonian diffeomorphisms $\mathrm{Ham}(M,\omega)$ in $\mathrm{Homeo}(M
Externí odkaz:
http://arxiv.org/abs/2311.12164
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 homotopy type of manifolds, with a view towards Floer theory. The model that
Externí odkaz:
http://arxiv.org/abs/2308.06104
Publikováno v:
Comptes Rendus. Mathematique, Volume 361 (2023), pp.1333--1340
We prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma$-support of $L$ coincides with the reduced micro-support of its sh
Externí odkaz:
http://arxiv.org/abs/2211.13945
In previous work, we defined "link spectral invariants" for any compact surface and used these to study the algebraic structure of the group of area-preserving homeomorphisms; in particular, we showed that the kernel of Fathi's mass-flow homomorphism
Externí odkaz:
http://arxiv.org/abs/2206.10749
Autor:
Cristofaro-Gardiner, Daniel, Humilière, Vincent, Mak, Cheuk Yu, Seyfaddini, Sobhan, Smith, Ivan
Publikováno v:
Forum of Mathematics, Pi. 2022;10:e27
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 invariant of Hamiltonians in their limit. As applications, we resolve
Externí odkaz:
http://arxiv.org/abs/2105.11026
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) we resolve the Kapovich-Polterovich question by showing that this gro
Externí odkaz:
http://arxiv.org/abs/2102.04404
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving homeomorphisms of the $n$-ball is simple for $n \ge 3$, asked if the same statement holds in dimension $2$. We show that the group of compactly supported area-
Externí odkaz:
http://arxiv.org/abs/2001.01792