Eduard Einstein
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View article: Hierarchies for relatively hyperbolic virtually special groups
Hierarchies for relatively hyperbolic virtually special groups Open
Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we con…
View article: Corrigendum to “Relatively geometric actions on CAT(0) cube complexes”
Corrigendum to “Relatively geometric actions on CAT(0) cube complexes” Open
We identify an error in E. Einstein and D. Groves [J. Lond. Math. Soc. (2), 105 (2022), no. 1, 691–708] which affects the construction of a completion and retraction of complexes of groups.
View article: Random Quotients of Free Products
Random Quotients of Free Products Open
We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with overwhelming probability: if the density is below $1/2$, the …
View article: On the boundary criterion for relative cubulation: multi-ended parabolics
On the boundary criterion for relative cubulation: multi-ended parabolics Open
In this note, we clarify that the boundary criterion for relative cubulation of the first author and Groves works even when the peripheral subgroups are not one-ended. Specifically, if the boundary criterion is satisfied for a relatively h…
View article: Walks with jumps: a neurobiologically motivated class of paths in the hyperbolic plane
Walks with jumps: a neurobiologically motivated class of paths in the hyperbolic plane Open
We introduce the notion of a "walk with jumps", which we conceive as an evolving process in which a point moves in a space (for us, typically $\mathbb{H}^2$) over time, in a consistent direction and at a consistent speed except that it is …
View article: Separation and relative quasiconvexity criteria for relatively geometric actions
Separation and relative quasiconvexity criteria for relatively geometric actions Open
Bowditch characterized relative hyperbolicity in terms of group actions on fine hyperbolic graphs with finitely many edge orbits and finite edge stabilizers. In this paper, we define generalized fine actions on hyperbolic graphs, in which …
View article: Relative Cubulation of Small Cancellation Free Products
Relative Cubulation of Small Cancellation Free Products Open
We expand the class of groups with relatively geometric actions on CAT(0) cube complexes by proving that it is closed under $C'(\frac16)$--small cancellation free products. We build upon a result of Martin and Steenbock who prove an analog…
View article: Separation and Relative Quasi-convexity Criteria for Relatively Geometric Actions
Separation and Relative Quasi-convexity Criteria for Relatively Geometric Actions Open
Bowditch characterized relative hyperbolicity in terms of group actions on fine hyperbolic graphs with finitely many edge orbits and finite edge stabilizers. In this paper, we define generalized fine actions on hyperbolic graphs, in which …
View article: Relatively geometric actions on CAT(0) cube complexes
Relatively geometric actions on CAT(0) cube complexes Open
We develop the foundations of the theory of relatively geometric actions of relatively hyperbolic groups on CAT(0) cube complexes, a notion introduced in our previous work [5]. In the relatively geometric setting we prove: full relatively …
View article: Relative cubulations and groups with a 2-sphere boundary
Relative cubulations and groups with a 2-sphere boundary Open
We introduce a new kind of action of a relatively hyperbolic group on a $\text{CAT}(0)$ cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of actions on cube…
View article: Ackermannian Integer Compression and the Word Problem for Hydra Groups
Ackermannian Integer Compression and the Word Problem for Hydra Groups Open
For a finitely presented group, the word problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is a complexity measure of a direct attack on the word problem by applyi…
View article: Ackermannian Integer Compression and the Word Problem for Hydra Groups.
Ackermannian Integer Compression and the Word Problem for Hydra Groups. Open
For a finitely presented group, the word problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is a complexity measure of a direct attack on the word problem by applyi…