Three dimensional FC Artin groups are CAT(0)
نویسنده
چکیده
Building upon earlier work of T. Brady, we construct locally CAT(0) classifying spaces for those Artin groups which are three dimensional and which satisfy the FC (flag complex) condition. The approach is to verify the “link condition” by applying gluing arguments for CAT(1) spaces and by using the curvature testing techniques of M. Elder and J. McCammond.
منابع مشابه
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 کامل2 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 کاملOn the CAT(0) dimension of 2-dimensional Bestvina-Brady groups
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...
متن کاملCAT(0) cubical complexes for graph products of finitely generated abelian groups
We construct for every graph product of finitely generated abelian groups a CAT(0) cubical complex on which it acts properly and cocompactly. The complex generalizes (up to subdivision) the Salvetti complex of a right-angled Artin group and the Coxeter complex of a right-angled Coxeter group.
متن کاملConnectivity at Infinity for Right Angled Artin Groups
We establish sufficient conditions implying semistability and connectivity at infinity properties for CAT(0) cubical complexes. We use this, along with the geometry of cubical K(π, 1)’s to give a complete description of the higher connectivity at infinity properties of right angled Artin groups. Among other things, this determines which right angled Artin groups are duality groups. Applications...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005