Seminar
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| Location: | SLMath: Online/Virtual |
To attend this seminar, please register here: https://www.msri.org/seminars/25205
Bounded cohomology is a mysterious tool that has been used to study nice isometric actions of discrete groups on symmetric spaces. We define bounded cohomology, volume classes, and investigate what these bounded cohomology classes can tell us about not-so-nice (dense) actions on hyperbolic 3-space. We exploit the rich and well studied theory of Kleinian groups, i.e. discrete subgroups of PSL_2(C), to give some geometric and topological meaning to the non-vanishing of the volume class associated to a dense representation of a discrete group into PSL_2(C). We note that our techniques have the potential to shed some light on volume classes associated to group actions on other symmetric spaces.
Volume Classes For Dense Actions Of Discrete Groups
To attend this seminar, please register here: https://www.msri.org/seminars/25205
Abstract:
Bounded cohomology is a mysterious tool that has been used to study nice isometric actions of discrete groups on symmetric spaces. We define bounded cohomology, volume classes, and investigate what these bounded cohomology classes can tell us about not-so-nice (dense) actions on hyperbolic 3-space. We exploit the rich and well studied theory of Kleinian groups, i.e. discrete subgroups of PSL_2(C), to give some geometric and topological meaning to the non-vanishing of the volume class associated to a dense representation of a discrete group into PSL_2(C). We note that our techniques have the potential to shed some light on volume classes associated to group actions on other symmetric spaces.
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Notes
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Volume Classes For Dense Actions Of Discrete Groups
| H.264 Video | 25399_28957_8529_Volume_Classes_for_Dense_Actions_of_Discrete_Groups.mp4 |