Ramón Flores, Delaram Kahrobaei, Thomas Koberda
We characterize $k$--colorability of a simplicial graph via the intrinsic algebraic structure of the associated right-angled Artin group. As a consequence, we show that a certain problem about the existence of homomorphisms from right-angled Artin groups to products of free groups is NP--complete.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Twisted right-angled Artin groups
该研究构建了扭化右角Artin群的完全重写系统，借助其导出的范式展开应用研究，对比了该类群与右角Artin群在几何、代数层面的异同。
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and algebraic properties in this extended setting. In particular, we characterise when these groups are locally compact, when they are abstractly simple, when they act primitively on residues of the building, and we discuss some necessary and sufficient conditions for the groups to be compactly generated. We point out that there are unexpected aspects related to the geo…
A finite simplicial graph Γdetermines a right-angled Artin group G_Γ, with generators corresponding to the vertices of Γ, and with a relation vw=wv for each pair of adjacent vertices. We compute the lower central series quotients, the Chen quotients, and the (first) resonance variety of G_Γ, directly from the graph Γ.
On the $\ell^2$-Betti numbers and algebraic fibring of the (outer) automorphism group of a right-angled Artin group
本文研究了右角Artin群的$\ell^2$-Betti数及外自同构群的代数纤维化特性，揭示了其非零条件与虚拟纤维化的关系。
We survey the relationship between the combinatorics and geometry of graphs and the algebraic structure of right-angled Artin groups. We concentrate on the defining graph of the right-angled Artin group and on the extension graph associated to the right-angled Artin group. Additionally, we discuss connections to geometric group theory and complexity theory. The final version of this survey will appear in "In the tradition of Thurston, vol.~II", ed.~K.~Ohshika and A.~Papadopoulos.
We study the algebraic structure of the automorphism group of a general right-angled Artin group. We show that this group is virtually torsion-free and has finite virtual cohomological dimension. This generalizes results proved by the authors and John Crisp (arXiv:math/0610980) for two-dimensional right-angled Artin groups.
The aim of this thesis is to present the notion of spaces whose curvature is bounded above, and to give some of its application in the context of Combinatorial Algebra. The thesis is made of two parts, one of theoretic purpose, and the other applicative. In particular, we present an application to the notion of $CAT(0)$-space and one to the Gromov Theorem for cubical complexes. In the final part we present a new class of discrete groups generalizing the well-known right-angled Artin groups. We concoct a cubical CAT(0)-complex on which the group acts, from whom we extract some algebraic propert…
We introduce a new quasi-isometry invariant of 2-dimensional right-angled Coxeter groups, the hypergraph index, that partitions these groups into infinitely many quasi-isometry classes, each containing infinitely many groups. Furthermore, the hypergraph index of any right-angled Coxeter group can be directly computed from the group's defining graph. The hypergraph index yields an upper bound for a right-angled Coxeter group's order of thickness, order of algebraic thickness and divergence function. Finally, given an integer n>1, we give examples of right-angled Coxeter groups which are thick o…
Conformal dimension bounds, Pontryagin sphere boundaries, and algebraic fibering of right-angled Coxeter groups
研究直角考克斯特群，通过引入\((n,m)\) - 分支条件构造组合圆树并嵌入戴维斯复形，给出双曲群边界共形维数下界，展示相关图族，证明嵌入结果，得出群的共形维数等结论，升级相关工作。
The Right Angled Artin Group Functor as a Categorical Embedding
本文证明可通过纯代数方式在群中刻画直角 Artin 群，并在群同态中刻画图同态，进而给出从 raag 恢复原图的新算法。
Algebraic and measurable embeddings between square-free right-angled Artin groups
本文证明无平方图上的右角Artin群之间的可测嵌入等价于子群嵌入到自由阿贝尔群的图积，并给出算法可检验的图论刻画及二维情形下的简化条件。
Dehn functions of mapping tori of right-angled Artin groups
本文研究直角 Artin 群在自同构下的代数映射环面，并对所有 3 生成元直角 Artin 群及 F_k × F_l（k,l ≥ 2）按自同构 Φ 分类其 Dehn 函数。
We survey the role of right-angled Artin groups in the theory of diffeomorphism groups of low dimensional manifolds. We first describe some of the subgroup structure of right-angled Artin groups. We then discuss the interplay between algebraic structure, compactness, and regularity for group actions on one--dimensional manifolds. For compact one--manifolds, every right-angled Artin group acts faithfully by $C^1$ diffeomorphisms, but the right-angled Artin groups which act faithfully by $C^2$ diffeomorphisms are very restricted. For the real line, every right-angled Artin group acts faithfully …
Presentation of kernels of rational characters of right-angled Artin groups
本文刻画直角 Artin 群有理特征标核的有限生成与有限表示条件，给出有限生成集及表示，推广并代数证明了相关经典结果。
We study the outer automorphism group of a right-angled Artin group A_G in the case where the defining graph G is connected and triangle-free. We give an algebraic description of Out(A_G) in terms of maximal join subgraphs in G and prove that the Tits' alternative holds for Out(A_G). We construct an analogue of outer space for Out(A_G) and prove that it is finite dimensional, contractible, and has a proper action of Out(A_G). We show that Out(A_G) has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most g…
Given a graph $Γ$, its auxiliary \emph{square-graph} $\square(Γ)$ is the graph whose vertices are the non-edges of $Γ$ and whose edges are the pairs of non-edges which induce a square (i.e., a $4$-cycle) in $Γ$. We determine the threshold edge-probability $p=p_c(n)$ at which the Erd{\H o}s--Rényi random graph $Γ=Γ_{n,p}$ begins to asymptotically almost surely have a square-graph with a connected component whose squares together cover all the vertices of $Γ_{n,p}$. We show $p_c(n)=\sqrt{\sqrt{6}-2}/\sqrt{n}$, a polylogarithmic improvement on earlier bounds on $p_c(n)$ due to Hagen and the autho…
Let $G$ be a free-by-cyclic group or a 2-dimensional right-angled Artin group. We provide an algebraic and a geometric characterization for when each aspherical simplicial complex with fundamental group isomorphic to $G$ has minimal volume entropy equal to 0. In the nonvanishing case, we provide a positive lower bound to the minimal volume entropy of an aspherical simplicial complex of minimal dimension for these two classes of groups. Our results rely upon a criterion for the vanishing of the minimal volume entropy for 2-dimensional groups with uniform uniform exponential growth. This criteri…
Conjugacy problem in virtual right-angled Artin groups
本文运用代数与几何方法，证明保长自同构构造的virtual RAAGs是CAT(0)群且共轭问题可解，推导其共轭增长级数的超越性，研究非保长情形实例，并解决保长自同构下RAAGs的扭曲共轭问题及部分算法复杂度。
We obtain a complete characterisation of factorial multiparameter Hecke von Neumann algebras associated with right-angled Coxeter groups. Considering their $\ell^p$-convolution algebra analogues, we exhibit an interesting parameter dependence, contrasting phenomena observed earlier for group Banach algebras. Translated to Iwahori-Hecke von Neumann algebras, these results allow us to draw conclusions on spherical representation theory of groups acting on right-angled buildings, which are in strong contrast to behaviour of spherical representations in the affine case. We also investigate certain…
We determine the precise conditions under which $\mathrm{SOut}(F_n)$, the unique index two subgroup of $\mathrm{Out}(F_n)$, can act non-trivially via outer automorphisms on a RAAG whose defining graph has fewer than $\frac 1 2 \binom n 2 $ vertices. We also show that the outer automorphism group of a RAAG cannot act faithfully via outer automorphisms on a RAAG with a strictly smaller (in number of vertices) defining graph. Along the way we determine the minimal dimensions of non-trivial linear representations of congruence quotients of the integral special linear groups over algebraically clos…
A characterization of virtually cyclic outer automorphism groups of right-angled Coxeter groups
本文研究了右角Coxeter群的外自同构群的虚循环性质，通过分析生成特定部分共轭的有限指数子群，确定了SILs、STILs和FSILs的存在与否对代数性质的影响。
For right-angled Coxeter groups $W_Γ$, we obtain a condition on $Γ$ that is necessary and sufficient to ensure that $W_Γ$ is thick and thus not relatively hyperbolic. We show that Coxeter groups which are not thick all admit canonical minimal relatively hyperbolic structures; further, we show that in such a structure, the peripheral subgroups are both parabolic (in the Coxeter group-theoretic sense) and strongly algebraically thick. We exhibit a polynomial-time algorithm that decides whether a right-angled Coxeter group is thick or relatively hyperbolic. We analyze random graphs in the Erdós-R…
The main theme of this paper is higher virtual algebraic fibering properties of right-angled Coxeter groups (RACGs), with a special focus on those whose defining flag complex is a finite building. We prove for particular classes of finite buildings that their random induced subcomplexes have a number of strong properties, most prominently that they are highly connected. From this we are able to deduce that the commutator subgroup of a RACG, with defining flag complex a finite building of a certain type, admits an epimorphism to $\mathbb{Z}$ whose kernel has strong topological finiteness proper…
Bestvina-Brady groups arise as kernels of length homomorphisms from right-angled Artin groups G_\G to the integers. Under some connectivity assumptions on the flag complex Δ_\G, we compute several algebraic invariants of such a group N_\G, directly from the underlying graph \G. As an application, we give examples of Bestvina-Brady groups which are not isomorphic to any Artin group or arrangement group.
Let $M$ be a compact one--manifold, and let $\mathrm{Diff}^{1+\mathrm{bv}}(M)$ denote the group of $C^1$ orientation preserving diffeomorphisms of $M$ whose first derivatives have bounded variation. We prove that if $G$ is a group which is not virtually metabelian, then $(G\times\mathbb{Z})*\mathbb{Z}$ is not realized as a subgroup of $\mathrm{Diff}^{1+\mathrm{bv}}(M)$. This gives the first examples of finitely generated groups $G,H\le \mathrm{Diff}_+^\infty(M)$ such that $G\ast H$ does not embed into $\mathrm{Diff}^{1+\mathrm{bv}}(M)$. By contrast, for all countable groups $G,H\le\mathrm{Home…
Lattice envelopes of right-angled Artin groups
本文构造非联图情形下直角 Artin 群的局部紧余紧格包络，并证明其半直积图自同构群为泛格包络，还刻画相关 Cayley 图全自同构群。
Improved algebraic fibrations of high-dimensional hyperbolic groups
对于每个 d≥3，通过右角Coxeter群的有限指数子群构造无穷多个上同调维数为d的双曲群G，它们具有有限表现核的代数纤维化，并利用L^2-Betti数给出核的更高有限性障碍。
Rotation groups, mediangle graphs, and periagroups: a unified point of view on Coxeter groups and graph products of groups
本文通过旋转群和中角图的统一视角，为Coxeter群和群的图积提供了统一的代数和几何研究框架，并给出了相关结果的统一证明。
The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups $\mathbb{G}(Δ)$ and $\mathbb{G}(Γ)$ are quasi-isometric, then $\mathbb{G}(Δ)$ is a (nice) subgroup of $\mathbb{G}(Γ)$ and vice-versa. We show that the conjecture holds for all known cases of quasi-isometric classification of partially commutative groups, namely for the classes of $n$-tress and atomic graphs. As in the classical Mostow rigidity theory for irre…
Divergence, thickness and hypergraph index for general Coxeter groups
研究一般Coxeter群的偏移量和厚度，定义可计算的超图指数，证明有限超图指数意味着厚度和偏移量的多项式界，提出拓扑学与超图指数的关系。
From algebraic orthogonality to RAAG embedding obstructions in hierarchically hyperbolic groups
该研究针对两类分层双曲群结构引入扩展核心图，证明直角阿廷群嵌入可经中间RAAG分解，给出RAAG嵌入障碍与判别准则，并建立相关不变性结果。
Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a small portion of the input. The most typical situation where sublinear time algorithms are considered is property testing. There are several interesting contexts where one can test properties in sublinear time. A canonical example is graph colorability. To tell that a given graph is not k-colorable, it is often sufficient to inspect just one vertex with incident edges: if the degree of a vertex is greater than k, then the graph is not k-colorable. It is a…
Isomorphism invariance of the girth of Artin groups
本文研究了Artin群的环长及其加权环长的同构不变性，揭示了其在不同图结构下的不变性质及计算方法。
Self-simulability of graph products
研究图积的自模拟性，证明无限有限生成群的图积自模拟当且仅当其定义图没有由可解群组成的分隔团，并应用于图积在可解子群上的分裂。
Cubical structures and the large-scale geometry of graph braid groups
本文通过立方结构研究图辫群的大规模几何，揭示其超几何性、未扭曲表面子群及群论分解，分类其与自由群的准等距关系，并探讨图2-辫群的准等距性质及相对超几何性新现象。
The power word problem for a group $G$ asks whether an expression $u_1^{x_1} \cdots u_n^{x_n}$, where the $u_i$ are words over a finite set of generators of $G$ and the $x_i$ binary encoded integers, is equal to the identity of $G$. It is a restriction of the compressed word problem, where the input word is represented by a straight-line program (i.e., an algebraic circuit over $G$). We start by showing some easy results concerning the power word problem. In particular, the power word problem for a group $G$ is $NC^1$-many-one reducible to the power word problem for a finite-index subgroup of …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。