Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative second bounded cohomology of free groups   This paper is devoted to the computation of the space
$H_b^2(\Gamma,H;\mathbb{R})$, where $\Gamma$ is a free group of finite rank
$n\geq 2$ and $H$ is a subgroup of finite rank. More precisely we prove that
$H$ has infinite index in $\Gamma$ if and only if $H_b^2(\Gamma,H;\mathbb{R})$
is not trivial, and furthermore, if and only if there is an isometric embedding
$\oplus_\infty^n\mathcal{D}(\mathbb{Z})\hookrightarrow
H_b^2(\Gamma,H;\mathbb{R})$, where $\mathcal{D}(\mathbb{Z})$ is the space of
bounded alternating functions on $\mathbb{Z}$ equipped with the defect norm.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics