Right?angled Artin subgroups of Artin groups

نویسندگان

چکیده

The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators any Artin group generate an obvious right-angled subgroup. We consider a larger set elements consisting all centers irreducible spherical special subgroups group, conjecture sufficiently large powers those This alleged subgroup is in some sense as possible; its nerve homeomorphic to ambient group. verify this for class locally reducible groups, which includes 2 $\hskip.001pt 2$ -dimensional groups type other than E 6 , 7 8 $E_6, E_7, E_8$ . use our results conclude certain contain hyperbolic surface subgroups, answering questions Gordon, Long Reid.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Convexity of parabolic subgroups in Artin groups

We prove that any standard parabolic subgroup of any Artin group is convex with respect to the standard generating set.

متن کامل

Surface subgroups of Coxeter and Artin groups

We prove that any Coxeter group that is not virtually free contains a surface group. In particular if the Coxeter group is word hyperbolic and not virtually free this establishes the existence of a hyperbolic surface group, and answers in the affirmative a question of Gromov in this setting. We also discuss when Artin groups contain hyperbolic surface groups. 2000 Mathematics Subject Classifica...

متن کامل

Surface Subgroups of Right-Angled Artin Groups

We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group A(K) has such a subgroup if its defining graph K contains an n-hole (i.e. an induced cycle of length n) with n ≥ 5. We construct another eight “forbidden” graphs and show that every graph K on ≤ 8 vertices either contains one of our examples, or co...

متن کامل

Right-angled Artin Groups and Their Subgroups

These are notes for a course offered at Yale University in the spring semester of 2013.

متن کامل

Constructing Presentations of Subgroups of Right-angled Artin Groups

Let G be the right-angled Artin group associated to the flag complex Σ and let π : G → Z be its canonical height function. We investigate the presentation theory of the groups Γn = π(nZ) and construct an algorithm that, given n and Σ, outputs a presentation of optimal deficiency on a minimal generating set, provided Σ is triangle-free; the deficiency tends to infinity as n → ∞ if and only if th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of the London Mathematical Society

سال: 2022

ISSN: ['1469-7750', '0024-6107']

DOI: https://doi.org/10.1112/jlms.12586