Timeline for Groups for which quasimorphisms are close to homomorphisms
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 21, 2019 at 20:52 | answer | added | Lvzhou Chen | timeline score: 1 | |
| Aug 12, 2019 at 4:05 | comment | added | tessellation | One big class for which kernel of $c$ is zero is lattices in higher rank lie groups. This is a theorem due to Burger and Monod. Bavard duality theorem states that space of non-trivial homogeneous quasimorphisms (i.e. the kernel of $c$) is trivial if and only if the stable commutator length (scl) of $G$ is zero. scl has been studied by various people for a large class of group. See ams.org/notices/200809/tx080901100p.pdf | |
| Aug 9, 2019 at 17:44 | comment | added | Zestylemonzi | Great reference/comment, cheers. | |
| Aug 9, 2019 at 11:13 | comment | added | YCor | Epstein and Fujiwara (link) proved that for $G$ non-elementary hyperbolic, $H^2_b(G,\mathbf{R})$ has continuum dimension. Since $H^2(G,\mathbf{R})$ is finite-dimensional for $G$ finitely presented, it shows that $c_G=c$ has a huge kernel for $G$ non-elementary hyperbolic. | |
| Aug 9, 2019 at 11:09 | history | edited | YCor | CC BY-SA 4.0 |
formatting; added full definition
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| Aug 9, 2019 at 10:24 | history | asked | Zestylemonzi | CC BY-SA 4.0 |