Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homology and topological full groups of etale groupoids on totally
  disconnected spaces   For almost finite groupoids, we study how their homology groups reflect
dynamical properties of their topological full groups. It is shown that two
clopen subsets of the unit space has the same class in H_0 if and only if there
exists an element in the topological full group which maps one to the other. It
is also shown that a natural homomorphism, called the index map, from the
topological full group to H_1 is surjective and any element of the kernel can
be written as a product of four elements of finite order. In particular, the
index map induces a homomorphism from H_1 to K_1 of the groupoid C^*-algebra.
Explicit computations of homology groups of AF groupoids and etale groupoids
arising from subshifts of finite type are also given.

9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th