The Geometry of Outer Automorphism Groups of Universal Right-angled Coxeter Groups Charles Cunningham, Haverford College Note the special date and time.
Abstract: We investigate the combinatorial and geometric properties of automorphism groups of universal right-angled Coxeter groups. McCullough-Miller space is a polyhedral complex which is virtually a geometric model for the outer automorphism group of a universal right-angled Coxeter group, $Out(W_n)$. As it is currently an open question as to whether or not $Out(W_n)$ is CAT(0) or not, it would be helpful to know whether McCullough-Miller space can always be equipped with an $Out(W_n)$-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).
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