Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditions on the monodromy for a surface group extension to be CAT(0)   In order to determine when surface-by-surface bundles are non-positively
curved, Llosa Isenrich and Py in \cite{Py} give a necessary condition: given a
surface-by-surface group $G$ with infinite monodromy, if $G$ is CAT(0) then the
monodromy representation is injective. We extend this to a more general result:
Let $G$ be a group with a normal surface subgroup $R$. Assume $G/R$ satisfies
the property that for every infinite normal subgroup $\Lambda$ of $G/R$, there
is an infinite subgroup $\Lambda_0<\Lambda$ so that the centralizer
$C_{G/R}(\Lambda_0)$ is finite. If $G$ is CAT(0) with infinite monodromy, then
the monodromy representation has a finite kernel. We prove that acylindrically
hyperbolic groups satisfy this property.

22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an