Dynamics on flag manifolds : domains of proper discontinuity and cocompactness
Kapovich, Michael (University of California at Davis)
Leeb, Bernhard (Universität München)
Porti, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2017
Resum:	For noncompact semisimple Lie groups G with finite center, we study the dynamics of the actions of their discrete subgroups Γ < G on the associated partial flag manifolds G/P. Our study is based on the observation, already made in the deep work of Benoist, that they exhibit also in higher rank a certain form of convergence-type dynamics. We identify geometrically domains of proper discontinuity in all partial flag manifolds. Under certain dynamical assumptions equivalent to the Anosov subgroup condition, we establish the cocompactness of the T-action on various domains of proper discontinuity, in particular on domains in the full flag manifold G/B. In the regular case (eg of B-Anosov subgroups), we prove the nonemptiness of such domains if G has (locally) at least one noncompact simple factor not of the type A1, B2 or G2 by showing the nonexistence of certain ball packings of the visual boundary.
Ajuts:	Ministerio de Economía y Competitividad MTM2012-34834 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-1207
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Anosov subgroups ; Cocompact actions ; Properly discontinuous actions
Publicat a:	Geometry and Topology, Vol. 22, Issue 1 (October 2017) , p. 157-234, ISSN 1364-0380

DOI: 10.2140/gt.2018.22.157

Postprint 66 p, 686.7 KB

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