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Seminar

RAS - Minicourse: Volume classes for dense actions of discrete groups September 30, 2020 (10:30 AM PDT - 11:30 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) James Farre (Yale University)
Description

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. 

Video

Volume Classes For Dense Actions Of Discrete Groups

Abstract/Media

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. 

Asset no preview Notes 9.1 MB application/pdf

Volume Classes For Dense Actions Of Discrete Groups

H.264 Video 25399_28957_8529_Volume_Classes_for_Dense_Actions_of_Discrete_Groups.mp4