Daniel Groves
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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: Homomorphisms to 3–Manifold Groups
Homomorphisms to 3–Manifold Groups Open
We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3–manifolds and answer questions of Agol–Liu (J. Am. Math. Soc. 25(1):151–187, 2012) and Re…
View article: Relatively geometric actions of Kähler groupson CAT(0) cube complexes
Relatively geometric actions of Kähler groupson CAT(0) cube complexes Open
View article: Drilling hyperbolic groups
Drilling hyperbolic groups Open
Given a hyperbolic group $G$ and a maximal infinite cyclic subgroup $\langle g \rangle$, we define a drilling of $G$ along $g$, which is a relatively hyperbolic group pair $(\widehat{G}, P)$. This is inspired by the well-studied procedure …
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: Hyperbolic groups acting improperly
Hyperbolic groups acting improperly Open
In this paper we study hyperbolic groups acting on CAT(0) cube complexes. The\nfirst main result (Theorem A) is a structural result about the Sageev\nconstruction, in which we relate quasi-convexity of hyperplane stabilizers with\nquasi-co…
View article: Relative cubulation of relative strict hyperbolization
Relative cubulation of relative strict hyperbolization Open
We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a CAT(0) cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite an…
View article: Special IMM groups
Special IMM groups Open
Italiano–Martelli–Migliorini recently constructed hyperbolic groups which have non‐hyperbolic subgroups of finite type. Using a closely related construction, Llosa Isenrich–Martelli–Py constructed hyperbolic groups with subgroups of type b…
View article: Special IMM groups
Special IMM groups Open
Italiano-Martelli-Migliorini recently constructed hyperbolic groups which have non-hyperbolic subgroups of finite type. Using a closely related construction, Llosa Isenrich-Martelli-Py constructed hyperbolic groups with subgroups of type $…
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: Homomorphisms to 3-manifold groups
Homomorphisms to 3-manifold groups Open
We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3-manifolds and answer questions of Reid-Wang-Zhou and Agol-Liu.
View article: Quasiconvexity and Dehn filling
Quasiconvexity and Dehn filling Open
We define a new condition on relatively hyperbolic Dehn filling which allows us to control the behavior of a relatively quasiconvex subgroups which need not be full. As an application, in combination with a recent result of Cooper and Fute…
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: Prescribed virtual homological torsion of 3-manifolds
Prescribed virtual homological torsion of 3-manifolds Open
We prove that given any finite abelian group $A$ and any irreducible $3$-manifold $M$ with empty or toroidal boundary which is not a graph manifold there exists a finite cover $M' \to M$ so that $A$ is a direct factor in $H_1(M',\mathbb{Z}…
View article: Specializing cubulated relatively hyperbolic groups
Specializing cubulated relatively hyperbolic groups Open
In arXiv:1204.2810 Agol proved the Virtual Haken and Virtual Fibering Conjectures by confirming a conjecture of Wise: Every cubulated hyperbolic group is virtually special. We extend this result to cocompactly cubulated relatively hyperbol…
View article: Investigating the catalytic mechanism of microtubule-severing enzymes
Investigating the catalytic mechanism of microtubule-severing enzymes Open
View article: Investigating the catalytic mechanism of microtubule-severing enzymes
Investigating the catalytic mechanism of microtubule-severing enzymes Open
View article: Investigating the catalytic mechanism of microtubule-severing enzymes
Investigating the catalytic mechanism of microtubule-severing enzymes Open
View article: Investigating the catalytic mechanism of microtubule-severing enzymes
Investigating the catalytic mechanism of microtubule-severing enzymes Open
View article: Investigating the catalytic mechanism of microtubule-severing enzymes
Investigating the catalytic mechanism of microtubule-severing enzymes Open
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: Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families
Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families Open
We study the set of homomorphisms from a fixed finitely generated group into a family of groups which are ‘uniformly acylindrically hyperbolic’. Our main results reduce this study to sets of homomorphisms which do not diverge in an appro…
View article: Abelian splittings of right-angled Artin groups
Abelian splittings of right-angled Artin groups Open
We characterize when (and how) a Right-Angled Artin group splits nontrivially over an abelian subgroup.
View article: Hyperbolic groups acting improperly
Hyperbolic groups acting improperly Open
In this paper we study hyperbolic groups acting on CAT(0) cube complexes. The first main result (Theorem A) is a structural result about the Sageev construction, in which we relate quasi-convexity of hyperplane stabilizers with quasi-conve…
View article: The structure of limit groups over hyperbolic groups
The structure of limit groups over hyperbolic groups Open
View article: The structure of limit groups over hyperbolic groups
The structure of limit groups over hyperbolic groups Open
View article: Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families
Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families Open
We study the set of homomorphisms from a fixed finitely generated group into a family of groups which are `uniformly acylindrically hyperbolic'. Our main results reduce this study to sets of homomorphisms which do not diverge in an appropr…
View article: Homomorphisms to acylindrically hyperbolic groups I: Equationally\n noetherian groups and families
Homomorphisms to acylindrically hyperbolic groups I: Equationally\n noetherian groups and families Open
We study the set of homomorphisms from a fixed finitely generated group into\na family of groups which are `uniformly acylindrically hyperbolic'. Our main\nresults reduce this study to sets of homomorphisms which do not diverge in an\nappr…
View article: Immutability is not uniformly decidable in hyperbolic groups
Immutability is not uniformly decidable in hyperbolic groups Open
A finitely generated subgroup H of a torsion-free hyperbolic group G is called immutable if there are only finitely many conjugacy classes of injections of H into G. We show that there is no uniform algorithm to recognize immutability, ans…
View article: Immutability is not uniformly decidable in hyperbolic groups
Immutability is not uniformly decidable in hyperbolic groups Open
A finitely generated subgroup H of a torsion-free hyperbolic group G is called immutable if there are only finitely many conjugacy classes of injections of H into G. We show that there is no uniform algorithm to recognize immutability, ans…