Groups & Dynamics Seminar

In order to generalize the geometry and dynamics of quasi-Fuchsian groups, the notion of Anosov subgroups has arisen as a powerful analogue. Using their north-south pole dynamics, Guichard–Wienhard and Kapovich–Leeb–Porti independently showed that Anosov subgroups admit cocompact domains of discontinuity inside flag varieties by thickening their limit sets. Alessandrini, Maloni, Tholozan, and Wienhard showed that such domains for certain Anosov surface subgroups admit a fiber bundle structure over the hyperbolic plane. In this talk, I will present a explicit description of this fiber as the boundary of a regular neighborhood over the thickening used to construct the domain. As an application to domains in the full flag variety, I exhibit a pair of Anosov surface subgroups inside SL(4,R) whose domains of discontinuity have non-isomorphic fundamental groups.