Geometry of pseudocharacters

By J. Manning. 2003

100 citations recorded by the source corpus.

If G is a group, a pseudocharacter f : G → R is a function which is “almost” a homomorphism. If G admits a nontrivial pseudocharacter f, we define the space of ends of G relative to f and show that if the space of ends is complicated enough, then G contains a nonabelian free group. We also construct a quasiaction by G on a tree whose space of ends contains the space of ends of G relative to f. This construction gives rise to examples of “exotic” quasi-actions on trees.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fed8cb403d8062ccb0927036edcf169915b1210d

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Citations in the corpus

Embedability between right-angled Artin groups (2011, background): “4 (Manning [27]) A geodesic metric space .”
Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “On the other hand, there is an evidence that for finitely presented groups, existence of non-trivial quasi-cocyclesmay be used to construct non-elementary actions on hyperbolic spaces [61].”
Growth tight actions (2014, background): “Manning [31] gave a characterization of quasi-trees as spaces satisfying a ‘bottleneck’ property.”
Stable commutator length on mapping class groups (2013, background): “It is a theorem of Manning [31] that a graph Q is a quasi-tree if and only if it satisfies the bottleneck property: there is a number ∆ > 0 (referred to as a bottleneck constant) such that any two vertices x, y ∈ Q are connected by a path α with the property that any other path connecting x to y nec”
Constructing group actions on quasi-trees and applications to mapping class groups (2010, background): “s follows directly from Proposition 2.8. By Lemma 2.6, dZ(Xk−2,Xk−1) ∼ 0 and dZ(Xk−1,Xk) ∼ 0 so the general statement then follows from the coarse triangle inequality. 2.4 PK(Y)is a quasi-tree Recall [Man05] that a geodesic metric space X satisﬁes the bottleneck property if there is a constant ∆ ≥ 0”
Weak hyperbolicity of cube complexes and quasi‐arboreal groups (2011, methodology): “1 can be deduced from Manning’s ‘bottleneck’ condition characterizing quasi-trees [27]; we also give a more constructive proof using disk diagram techniques, by constructing a graded root tree T and exhibiting a quasi-isometry Γ → T which grades the hyperplanes by the distances of their images to a ”
Hyperbolicities in CAT(0) cube complexes (2017, unknown): “In particular, our goal is to apply the bottleneck criterion [Man05]:”
The asymptotic dimension of a curve graph is finite (2005, background): “. Connect the (reduced) fractions p/q and r/s by an edge precisely when |ps−rq| = 1. The resulting graph is connected and each edge separates the graph. The following result appears as Example 5.2 in [35], where Manning uses an interesting condition called the bottleneck property. Proposition1([35])”
Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees (2004, methodology): “y quasiaction on a tree arises, as in the above lemma, from an action on an R-tree. But before we ever distributed this paper, Jason Manning had anticipated the question and produced counter-examples [Man05] — he produces quasi-actions on trees of groups which cannot act non-trivially on R-trees. Ex”
Asymptotic Dimension (2007, background): “There, the proof appeals to Manning’s bottle-neck property, [72].”