Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Actions of Cremona groups on CAT(0) cube complexes   For each d we construct CAT(0) cube complexes on which Cremona groups rank d
act by isometries. From these actions we deduce new and old group theoretical
and dynamical results about Cremona groups. In particular, we study the
dynamical behaviour of the irreducible components of exceptional loci, we prove
regularization theorems, we find new constraints on the degree growth for
non-regularizable birational transformations, and we show that the centralizer
of certain birational transformations is small.

6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc