University of Sydney Algebra Seminar
Marc Burger
Friday 10 Mar, 12-1pm, Place: Carslaw 173
On the Real Spectrum Compactification of Character Varieties
For a finitely generated group F and a real algebraic semisimple group G, the set of conjugacy classes of G-representations of F is naturally a real semialgebraic set, called the G-character "variety" of F. For instance when F is the fundamental group of a closed surface then, depending on G, certain connected components of the G-character variety of F consist entirely of injective representations with discrete image: these are the so called "higher Teichmueller spaces". The real spectrum of a real algebraic set provides then a compactification of all its semialgebraic subsets and leads to interesting compactifications of higher Teichmueller spaces. I will describe some of the properties of these compactifications and relate them to other known compactifications. This is part of an ongoing project with Alessandra Iozzi, Anne Parreau and Beatrice Pozzetti.