Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Central extensions and bounded cohomology   It was shown by Gersten that a central extension of a finitely generated
group is quasi-isometrically trivial provided that its Euler class is bounded.
We say that a finitely generated group $G$ satisfies Property QITB
(quasi-isometrically trivial implies bounded) if the Euler class of any
quasi-isometrically trivial central extension of $G$ is bounded. We exhibit a
finitely generated group $G$ which does not satisfy Property QITB. This answers
a question by Neumann and Reeves, and provides partial answers to related
questions by Wienhard and Blank. We also prove that Property QITB holds for a
large class of groups, including amenable groups, right-angled Artin groups,
relatively hyperbolic groups with amenable peripheral subgroups, and 3-manifold
groups.
  Finally, we show that Property QITB holds for every finitely presented group
if a conjecture by Gromov on bounded primitives of differential forms holds as
well.

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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an