On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups

نویسنده

  • John Crisp
چکیده

Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the ‘Bestvina-Brady group’, or ‘Artin kernel’, ΓK . We show that ΓK has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. Different choices of K lead to examples where the CAT(0) dimension is 3, and either (i) the geometric dimension is 2, or (ii) the cohomological dimension is 2 and the geometric dimension is not known. AMS Classification 20F67; 57M20

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Bestvina-Brady Groups and the Plus Construction

A recent result of Bestvina and Brady [1], Theorem 8.7, shows that one of two outstanding questions has a negative answer: either there exists a group of cohomological dimension 2 and geometric dimension 3 (a counterexample to the Eilenberg-Ganea Conjecture [4]), or there exists a nonaspherical subcomplex of an aspherical 2-complex (a counterexample to the Whitehead Conjecture [11]). More preci...

متن کامل

Two-dimensional Artin Groups with Cat(0) Dimension Three *

We exhibit 3-generator Artin groups which have finite 2-dimensional Eilenberg-Mac Lane spaces, but which do not act properly discontinuously by semi-simple isometries on a 2-dimensional CAT(0) complex. We prove that infinitely many of these groups are the fundamental groups of compact, non-positively curved 3-complexes. These examples show that the geometric dimension of a CAT(0) group may be s...

متن کامل

Cat(0) and Cat(-1) Dimensions of Torsion Free Hyperbolic Groups

We show that a particular free-by-cyclic group G has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. Starting from a fixed presentation 2-complex we define a family of non-positively curved piecewise Euclidean “model” spaces for G, and show that whenever the group acts properly by isometries on any proper 2-dimensional CAT(0) space X there exists a Gequivariant map from the unive...

متن کامل

2 Two - dimensional Artin groups with CAT ( 0 ) dimension three ∗

We exhibit 3-generator Artin groups which have finite 2-dimensional Eilenberg-Mac Lane spaces, but which do not act properly discontinuously by semi-simple isometries on a 2-dimensional CAT(0) complex. We prove that infinitely many of these groups are the fundamental groups of compact, non-positively curved 3-complexes. These examples show that the geometric dimension of a CAT(0) group may be s...

متن کامل

Algebraic Invariants for Bestvina-brady Groups

Bestvina-Brady groups arise as kernels of length homomorphisms GΓ → Z from right-angled Artin groups to the integers. Under some connectivity assumptions on the flag complex ∆Γ, we compute several algebraic invariants of such a group NΓ, directly from the underlying graph Γ. As an application, we give examples of finitely presented Bestvina-Brady groups which are not isomorphic to any Artin gro...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002