Seminar: Obstructing deformations between Anosov representations via homotopy type

Abstract: Anosov representations of closed surface groups have arisen as a higher-rank analogue of the quasi-Fuchsian representations. Among their shared dynamical properties is the existience of domains of discontinuity in flag varieties, proven by Guichard–Wienhard and Kapovich–Leeb–Porti, using a thickened limit set. Alessandrini, Maloni, Tholozan, and Wienhard showed that such domains for Anosov representations factoring through SL(2,R) admit a fiber bundle structure over the hyperbolic plane. In this talk, I will present a description of this fiber in the general case as the boundary of a regular neighborhood over the thickening. From this, we will look at how deforming the limit set can be used to compare fibers for different representations. As an application homomorphisms of SL(2,R) into SL(n,R) which restrict to 1-Anosov representations admit fibers with at most two homeomorphism types for each n≥5.