Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounded cohomology of discrete groups   Bounded cohomology of groups was first defined by Johnson and Trauber during
the seventies in the context of Banach algebras. As an independent and very
active research field, however, bounded cohomology started to develop in 1982,
thanks to the pioneering paper "Volume and Bounded Cohomology" by M. Gromov,
where the definition of bounded cohomology was extended to deal also with
topological spaces.
  The aim of this monograph is to provide an introduction to bounded cohomology
of discrete groups and of topological spaces. We also describe some
applications of the theory to related active research fields (that have been
chosen according to the taste and the knowledge of the author). The book is
essentially self-contained. Even if a few statements do not appear elsewhere
and some proofs are slighlty different from the ones already available in the
literature, the monograph does not contain original results.
  In the first part of the book we settle the fundamental definitions of the
theory, and we prove some (by now classical) results on low-dimensional bounded
cohomology and on bounded cohomology of topological spaces. Then we describe
how bounded cohomology has proved useful in the study of the simplicial volume
of manifolds, for the classification of circle actions, for the definition and
the description of maximal representations of surface groups, and in the study
of higher rank flat vector bundles (also in relation with the Chern
conjecture).

1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph