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papers

Publications (23)

math.GT2025

Embedding spaces of split links

Rachael Boyd, Corey Bregman

We study the homotopy type of the space $E (L)$ of unparametrised embeddings of a split link $L = L_{1} ⊔ \dots ⊔ L_{n}$ in $R^{3}$ . Our main result is a simple descripti…

math.GR2024

Finite groups of untwisted outer automorphisms of RAAGs

Corey Bregman, Ruth Charney, Karen Vogtmann

For any right-angled Artin group $A_{I^} $ , Charney--Stambaugh--Vogtmann showed that the subgroup $U^{0} (A_{I^} ) \leq Out (A_{I^} )$ generated by Whitehead automorphisms and inversions…

math.GT2024

On a generalization of Cannon's conjecture for cubulated hyperbolic groups

Corey Bregman, Merlin Incerti-Medici

We show that cubulated hyperbolic groups with spherical boundary of dimension 3 or at least 5 are virtually fundamental groups of closed, orientable, aspherical manifolds, provided…

math.GR2015

Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles

Corey Bregman

Given a matrix $A \in S L (N, Z)$ , form the semidirect product $G = Z^{N} ⋊_{A} Z$ where the $Z$ factor acts on $Z^{N}$ by $A$ . Such a $G$ arises naturally as the fundamental group o…

math.GT2016

Automorphisms and homology of non-positively curved cube complexes

Corey Bregman

We define an integer-valued invariant of special cube complexes called the genus, and prove that having genus one characterizes special cube complexes with abelian fundamental grou…

math.GT2016

On Kahler extensions of abelian groups

Corey Bregman, Letao Zhang

We show that any Kahler extension of a finitely generated abelian group by a surface group of genus g at least 2 is virtually a product. Conversely, we prove that any homomorphism…