The outer space of a free product
By Vincent Guirardel, Gilbert Levitt. 2005
108 citations recorded by the source corpus.
We associate a contractible ‘outer space’ to any free product of groups G = G1 * … * Gq. It is identical to Culler–Vogtmann space when G is free, and McCullough–Miller space when no Gi is ℤ. Our proof of contractibility (given when G is not free) is based on Skora's idea of deforming morphisms between trees.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d0c9172344d8c8b260ab97b3ff69ba9e007389e8
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Vincent Guirardel
- Anthony Genevois
- Gilbert Levitt
- Karen Vogtmann
- Alexandre Martin
- Ruth Charney
- Ilya Kapovich
- Alessandro Sisto
In Mathematical Physics
- Gilbert Levitt
- Vincent Guirardel
- Anthony Genevois
- Ruth Charney
- Karen Vogtmann
- Alexandre Martin
- M. Bestvina
- Ilya Kapovich
Citations in the corpus
- Axes in Outer Space (2006, unknown): “Fold lines. Fold lines form a natural class of paths in outer space arising from several concepts: train track maps due to Bestvina and Handel [BH92]; Stallings folds [Sta83]; and semiflow concepts behind Skora’s method for investigating homotopy properties of spaces of R-trees ([Sko], and see also ”
- On the automorphism group of generalized Baumslag–Solitar groups (2005, background): “In general, there are several ways to define a topology on spaces of trees (equivariant Gromov–Hausdorff topology, axes topology, weak topology), but because of local finiteness they all coincide on PD (see the discussion in Guirardel–Levitt [16; 17]).”
- Jsj Decompositions of Groups (2016, unknown): “rmationspace LetAconsistonlyofthetrivialsubgroupof G,andH= ;. ThusA-treesaretreeswith trivialedgestabilizers,alsocalled free splittings. ThentheJSJdeformationspaceexists, itistheouterspaceintroducedin[GL07b](see[CV86]whenG= F n,and[MM96]when nofreefactorofGisZ). WecallittheGrushkodeformationspace. I”
- Finiteness properties of automorphism groups of right‐angled Artin groups (2009, background): “However, in this case, we do not have the analog of theorem [6] to pass from the connected to the disconnected case.”
- Splittings and automorphisms of relatively hyperbolic groups (2012, methodology): “y component to itself in an orientation-preserving way, and GLr,n(Z) = Mr,n(Z) ⋊GLr(Z) is the group of automorphisms of Zn+r fixing the first n generators. See Theorem 5.3 of [BKM07] and Theorem 6.5 of [GL07b] for the case of limit groups, based on results from [KM05] and [BKM07]. Proof. We may assume”
- Automorphisms of graph products of groups from a geometric perspective (2018, background): “Most of the literature on this topic imposes very strong conditions on the graph products involved, either on the underlying graph (as in the case of the automorphisms groups of free products [22, 29, 30]) or on the vertex groups (most of the case, they are required to be abelian or even cyclic [11,”
- Deformation spaces of trees (2006, methodology): “Examples of deformation spaces are Culler-Vogtmann’s outer space [12], as well as spaces constructed by McCullough-Miller [26] and the authors [ 20 ] to study automorphisms of free products, and the canonical set of splittings of generalized Baumslag-Solitar groups [18, 25].”