Automorphisms of Free Groups and Outer Space

By Karen Vogtmann. 2002

191 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fd377676d84354021245541b786c12a441e5ccfe

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Intersection Form, Laminations and Currents on Free Groups (2007, background): “(4) The quotient Y = Ts/F is a finite reduced graph of groups where the vertex groups correspond to setwise F -stabilizers of trees from V and where the edge-lengths correspond to distances in T between F -orbits of the trees from V representing the end-points of the edge in question.”
Cohomological structure of the mapping class group and beyond (2005, background): “Recently many works have been done on the structure of Out Fn as well as Gn, notably by Vogtmann (see her survey paper [106]), Bestvina (see [2]) and many others.”
Homogeneous trees of second order Sturm-Liouville equations: A general theory and program (2008, background): “An interesting moduli space of metric graphs(4) with a fixed fundamental group was introduced twenty years ago in [56] (see also [34, 136] and the survey [210]).”
The outer space of a free product (2005, background): “A different approach was introduced by Culler-Vogtmann [9], who obtained finiteness results for Out(Fn) by letting it act on a contractible complex now known as outer space (see [30]).”
Algebraic and tropical curves: comparing their moduli spaces (2011, background): “For example, using what is known for the outer space Og (see the survey [26]) one may construct bordifications of the moduli space of pure tropical curves other than the one we described in the present paper (via weighted, or extended tropical curves).”
METRIC PROPERTIES OF OUTER SPACE (2008, background): “We refer the reader to [10] for an excellent survey and refere nce article to Culler-Vogtmann space.”
Dimension of the Torelli group for Out(Fn) (2006, methodology): “This question was explicitly asked by Vogtmann in her survey article [14].”
Axes in Outer Space (2006, unknown): “1.3 A question of Vogtmann. In [ Vog02 ] Vogtmann asked:”
The hyperbolicity of the sphere complex via surgery paths (2012, background): “The maximal number of spheres in a sphere system is equal to 3n − 3 (this is the dimension of Culler and Vogtmann’s unprojectivized Outer space, see [24] for instance).”
Constructing group actions on quasi-trees and applications to mapping class groups (2010, methodology): “continuous. (5) G = Out(Fn) acting on Culler-Vogtmann’s Outer space CV [CV86], equipped with the Lipschitz metric (which fails to be symmetric, see [AKB12]). The action is properly discontinuous. See [Vog02], [BV06], [Vog06] for more information on Out(Fn) and Outer space. An element f of Out(Fn) is”
The Patterson–Sullivan Embedding and Minimal Volume Entropy for Outer Space (2005, methodology): “We refer the reader to the original paper [12] and to a survey paper [ 39 ] for a detailed discussion of the basic facts listed in this section and for the further references.”
The actions of ${\mathit{Out}(F_k)}$ on the boundary of Outer space and on the space of currents: minimal sets and equivariant incompatibility (2006, background): “Conventions regarding Outer space We refer the reader to [1, 10, 11, 13, 27] for detailed information regarding Outer space and its boundary.”