Hyperbolic actions and 2nd bounded cohomology of subgroups of $\text{Out}(F_n)$. Part I: Infinite lamination subgroups
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arXiv
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| Format: | Preprint |
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2015
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| _version_ | 1866913728366116864 |
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| author | Handel, Michael Mosher, Lee |
| author_facet | Handel, Michael Mosher, Lee |
| contents | In this two part work we prove that for every finitely generated subgroup $Γ< \text{Out}(F_n)$, either $Γ$ is virtually abelian or $H^2_b(Γ;\mathbb{R})$ contains an embedding of $\ell^1$. The method uses actions on hyperbolic spaces, for purposes of constructing quasimorphisms. Here in Part I, after presenting the general theory, we focus on the case of infinite lamination subgroups $Γ$ - those for which the set of all attracting laminations of all elements of $Γ$ is infinite - using actions on free splitting complexes of free groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1511_06913 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Hyperbolic actions and 2nd bounded cohomology of subgroups of $\text{Out}(F_n)$. Part I: Infinite lamination subgroups Handel, Michael Mosher, Lee Group Theory 20F65 (primary) 57M07 (secondary) In this two part work we prove that for every finitely generated subgroup $Γ< \text{Out}(F_n)$, either $Γ$ is virtually abelian or $H^2_b(Γ;\mathbb{R})$ contains an embedding of $\ell^1$. The method uses actions on hyperbolic spaces, for purposes of constructing quasimorphisms. Here in Part I, after presenting the general theory, we focus on the case of infinite lamination subgroups $Γ$ - those for which the set of all attracting laminations of all elements of $Γ$ is infinite - using actions on free splitting complexes of free groups. |
| title | Hyperbolic actions and 2nd bounded cohomology of subgroups of $\text{Out}(F_n)$. Part I: Infinite lamination subgroups |
| topic | Group Theory 20F65 (primary) 57M07 (secondary) |
| url | https://arxiv.org/abs/1511.06913 |