0000000000186570
AUTHOR
Sang-hyun Kim
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 eige…
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Gislason, Gunnar H/0000-0002-0548-402X; Malynovsky, Yaroslav V/0000-0002-9118-1104; Bhatt, Deepak L./0000-0002-1278-6245; Nikolaev, Konstantin/0000-0003-4601-6203; Sherwood, Matthew/0000-0002-4305-5883; Chumakova, Galina A/0000-0002-2810-6531; Raffel, Owen C/0000-0001-5470-7050; Leonardi, Sergio/0000-0002-4800-6132; Tse, Hung Fat/0000-0002-9578-7808; Reshetko, Olga/0000-0003-3107-7636; Pereira, Helder/0000-0001-8656-4883; Racca, Vittorio/0000-0002-4465-3789; Podoleanu, Cristian/0000-0001-9987-2519; Ersanli, Murat/0000-0003-1847-3087; Muenzel, Thomas/0000-0001-5503-4150; Sandhu, Manjinder/0000-0003-2538-2079; Taskinen, Marja-Riitta/0000-0002-6229-3588; bastos, jose/0000-0002-9526-3123; Manak…