On the Automorphism Groups of Universal Right-Angled Coxeter Groups. - Cunningham, Charles. (2017)
Abstract: We investigate the combinatorial and geometric properties of automorphism groups of universal right-angled Coxeter groups. McCullough-Miller space is virtually a geometric model for the outer automorphism group of a universal right-angled Coxeter group, Out(Wn). As it is currently an open question as to whether or not Out(Wn) is CAT(0) or not, it would be helpful to know whether McCullough-Miller space can always be equipped with an Out(Wn)-equivariant CAT(0) metric. We show that the answer is in the negative. This is particularly interesting as there are very few non-trivial examples of proving that a space of independent interest is not CAT(0). We also show that an otherwise promising finite index subgroup of Out(Wn) is not a right-angled Coxeter group.; Thesis (Ph.D.)--Tufts University, 2015.; Submitted to the Dept. of Mathematics.; Advisor: Kim Ruane.; Committee: Ruth Charney, Genevieve Walsh, Mauricio Gutierrez, and Kim Ruane.; Keyword: Mathematics.