Cocycle superrigidity from higher rank lattices to Out(F_N)

Autor: Vincent Guirardel, Camille Horbez, Jean Lécureux

Publikováno v: Journal of modern dynamics
Journal of modern dynamics, 2022, 18, pp.291-344. ⟨10.3934/jmd.2022010⟩

We prove a rigidity result for cocycles from higher rank lattices to $\mathrm{Out}(F_N)$ and more generally to the outer automorphism group of a torsion-free hyperbolic group. More precisely, let $G$ be either a product of connected higher rank simpl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ade780199bbe64c7a3f9017bb6073a2
https://hal.archives-ouvertes.fr/hal-02611060/document

Vastness properties of automorphism groups of RAAGs

Autor: Vincent Guirardel, Andrew W. Sale

Publikováno v: Journal of Topology. 11:30-64

Outer automorphism groups of RAAGs, denoted $Out(A_\Gamma)$, interpolate between $Out(F_n)$ and $GL_n(\mathbb{Z})$. We consider several vastness properties for which $Out(F_n)$ behaves very differently from $GL_n(\mathbb{Z})$: virtually mapping onto

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::14b49cbbca1e407b73f5a76a4f975289
https://doi.org/10.1112/topo.12047

Boundaries of relative factor graphs and subgroup classification for automorphisms of free products

Autor: Vincent Guirardel, Camille Horbez

Publikováno v: Geometry and Topology
Geometry and Topology, 2022, 26 (1), pp.71-126. ⟨10.2140/gt.2022.26.71⟩

Given a countable group $G$ splitting as a free product $G=G_1\ast\dots\ast G_k\ast F_N$, we establish classification results for subgroups of the group $Out(G,\mathcal{F})$ of all outer automorphisms of $G$ that preserve the conjugacy classes of eac

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::616577a8413f0fea047f2be18e137284
https://hal.archives-ouvertes.fr/hal-02002080

Recognizing a relatively hyperbolic group by its Dehn fillings

Autor: François Dahmani, Vincent Guirardel

Publikováno v: Duke Math. J. 167, no. 12 (2018), 2189-2241
IF_PREPUB. 37 pages. 2015
Duke Mathematical Journal
Duke Mathematical Journal, Duke University Press, 2018, 167 (12), pp.2189-2241. ⟨10.1215/00127094-2018-0014⟩
Duke Mathematical Journal, 2018, 167 (12), pp.2189-2241. ⟨10.1215/00127094-2018-0014⟩

Dehn fillings for relatively hyperbolic groups generalize the topological Dehn surgery on a non-compact hyperbolic $3$-manifold such as a hyperbolic knot complement. We prove a rigidity result saying that if two non-elementary relatively hyperbolic g

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4200fcda72570428552a33433fa75d4c
https://projecteuclid.org/euclid.dmj/1532073620

Hyperbolic rigidity of higher rank lattices

Autor: Camille Horbez, Vincent Guirardel, Thomas Haettel

Publikováno v: Improved exposition, Appendix on "Morphisms from higher rank lattices to Out(F_N)" by Vincent Gui.. 2018
Annales Scientifiques de l'École Normale Supérieure
Annales Scientifiques de l'École Normale Supérieure, Société mathématique de France, 2020, 53 (2), pp.439-468. ⟨10.24033/asens.2425⟩
Annales Scientifiques de l'École Normale Supérieure, 2020, 53 (2), pp.439-468. ⟨10.24033/asens.2425⟩

We prove that any action of a higher rank lattice on a Gromov-hyperbolic space is elementary. More precisely, it is either elliptic or parabolic. This is a large generalization of the fact that any action of a higher rank lattice on a tree has a fixe

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df5a886e11aa4082dfbe8bb75366db6d
http://arxiv.org/abs/1607.02004