Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat