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Jingyin Huang

Publications and source records attributed to Jingyin Huang.

41 records · Page 3Linked to original sources
arXiv2016

Determining the action dimension of an Artin group by using its complex of abelian subgroups

Suppose that $(W,S)$ is a Coxeter system with associated Artin group $A$ and with a simplicial complex $L$ as its nerve. We define the notion of a "standard abelian subgroup" in $A$. The poset of such subgroups in $A$ is parameterized by the poset of simplices in a certain subdivision $L_\oslash$ of $L$. This complex of standard abelian subgroups is used to generalize an earlier result from the case of right-angled Artin groups to case of general Artin groups, by calculating, in many instances, the smallest dimension of a manifold model for $BA$. (This is the "action dimension" of $A$ denoted actdim $A$.) If $H_d(L; \mathbb Z/2)\neq 0$, where $d=\dim L$, then actdim $A \ge 2d+2$. Moreover, when the $K(π,1)$-Conjecture holds for $A$, the inequality is an equality.

math.GT↗
arXiv2016

Top dimensional quasiflats in $CAT(0)$ cube complexes

We show that every $n$-quasiflat in a $n$-dimensional $CAT(0)$ cube complex is at finite Hausdorff distance from a finite union of $n$-dimensional orthants. Then we introduce a class of cube complexes, called {\em weakly special} cube complexes and show that quasi-isometries between their universal coverings preserve top dimensional flats. We use this to establish several quasi-isometry invariants for right-angled Artin groups. Some of our arguments also extend to $CAT(0)$ spaces of finite geometric dimension. In particular, we give a short proof of the fact that a top dimensional quasiflat in a Euclidean buildings is Hausdorff close to finite union of Weyl cones, which was previously established in several other authors by different methods.

math.GR↗
arXiv2016

Commensurability of groups quasi-isometric to RAAG's

Let $G$ be a right-angled Artin group with defining graph $Γ$ and let $H$ be a finitely generated group quasi-isometric to $G(Γ)$. We show if $G$ satisfies (1) its outer automorphism group is finite; (2) $Γ$ does not have induced 4-cycle; (3) $Γ$ is star-rigid; then $H$ is commensurable to $G$. We show condition (2) is sharp in the sense that if $Γ$ contains an induced 4-cycle, then there exists an $H$ quasi-isometric to $G(Γ)$ but not commensurable to $G(Γ)$. Moreover, one can drop condition (1) if $H$ is a uniform lattice acting on the universal cover of the Salvetti complex of $G(Γ)$. As a consequence, we obtain a conjugation theorem for such uniform lattices. The ingredients of the proof include a blow-up building construction in \cite{cubulation} and a Haglund-Wise style combination theorem for certain class of special cube complexes. However, in most of our cases, relative hyperbolicity is absent, so we need new ingredients for the combination theorem.

math.GT↗
arXiv2016

Groups quasi-isometric to RAAG's

We characterize groups quasi-isometric to a right-angled Artin group $G$ with finite outer automorphism group. In particular all such groups admit a geometric action on a $CAT(0)$ cube complex that has an equivariant "fibering" over the Davis building of $G$.

math.GR↗