Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small $C^1$ actions of semidirect products on compact manifolds   Let $T$ be a compact fibered $3$--manifold, presented as a mapping torus of a
compact, orientable surface $S$ with monodromy $\psi$, and let $M$ be a compact
Riemannian manifold. Our main result is that if the induced action $\psi^*$ on
$H^1(S,\mathbb{R})$ has no eigenvalues on the unit circle, then there exists a
neighborhood $\mathcal U$ of the trivial action in the space of $C^1$ actions
of $\pi_1(T)$ on $M$ such that any action in $\mathcal{U}$ is abelian. We will
prove that the same result holds in the generality of an infinite cyclic
extension of an arbitrary finitely generated group $H$, provided that the
conjugation action of the cyclic group on $H^1(H,\mathbb{R})\neq 0$ has no
eigenvalues of modulus one. We thus generalize a result of A. McCarthy, which
addressed the case of abelian--by--cyclic groups acting on compact manifolds.

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The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat