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Articles

Affine Anosov Representations and Proper Actions

Published in Oxford University Press

2022

DOI: 10.1093/imrn/rnac232

Volume: 2023

Issue: 16

Pages: 14334 - 14367

We define the notion of affine Anosov representations of word hyperbolic groups into the affine group ${\mathsf{\text{SO}}}^{0}(\ufffd+1,\ufffd)\u22c9{\mathbb{\ufffd}}^{2\ufffd+1}$. We then show that a representation $\ufffd$ of a word hyperbolic group is affine Anosov if and only if its linear part ${\mathtt{\ufffd}}_{\ufffd}$ is Anosov in ${\mathsf{\text{SO}}}^{0}(\ufffd+1,\ufffd)$ with respect to the stabilizer of a maximal isotropic plane and $\ufffd(\mathrm{\Gamma})$ acts properly on ${\mathbb{\ufffd}}^{2\ufffd+1}$.We define the notion of affine Anosov representations of word hyperbolic groups into the affine group ${\mathsf{\text{SO}}}^{0}(\ufffd+1,\ufffd)\u22c9{\mathbb{\ufffd}}^{2\ufffd+1}$. We then show that a representation $\ufffd$ of a word hyperbolic group is affine Anosov if and only if its linear part ${\mathtt{\ufffd}}_{\ufffd}$ is Anosov in ${\mathsf{\text{SO}}}^{0}(\ufffd+1,\ufffd)$ with respect to the stabilizer of a maximal isotropic plane and $\ufffd(\mathrm{\Gamma})$ acts properly on ${\mathbb{\ufffd}}^{2\ufffd+1}$.

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About the journal

Journal | International Mathematics Research Notices |
---|---|

Publisher | Oxford University Press |

Open Access | No |