Hyperbolic actions and 2nd bounded cohomology of subgroups of $\mathsf{Out}(F_n)$. Part II: Finite lamination subgroups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866912268398100480 |
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| author | Handel, Michael Mosher, Lee |
| author_facet | Handel, Michael Mosher, Lee |
| contents | This is the second part of a two part work in which we prove that for every finitely generated subgroup $Γ< \mathsf{Out}(F_n)$, either $Γ$ is virtually abelian or its second bounded cohomology $H^2_b(Γ;\mathbb{R})$ contains an embedding of $\ell^1$. Here in Part II we focus on finite lamination subgroups $Γ$ --- meaning that the set of all attracting laminations of elements of $Γ$ is finite --- and on the construction of hyperbolic actions of those subgroups to which the general theory of Part I is applicable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1702_08050 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Hyperbolic actions and 2nd bounded cohomology of subgroups of $\mathsf{Out}(F_n)$. Part II: Finite lamination subgroups Handel, Michael Mosher, Lee Group Theory 20F65 (primary) 57M07 (secondary) This is the second part of a two part work in which we prove that for every finitely generated subgroup $Γ< \mathsf{Out}(F_n)$, either $Γ$ is virtually abelian or its second bounded cohomology $H^2_b(Γ;\mathbb{R})$ contains an embedding of $\ell^1$. Here in Part II we focus on finite lamination subgroups $Γ$ --- meaning that the set of all attracting laminations of elements of $Γ$ is finite --- and on the construction of hyperbolic actions of those subgroups to which the general theory of Part I is applicable. |
| title | Hyperbolic actions and 2nd bounded cohomology of subgroups of $\mathsf{Out}(F_n)$. Part II: Finite lamination subgroups |
| topic | Group Theory 20F65 (primary) 57M07 (secondary) |
| url | https://arxiv.org/abs/1702.08050 |