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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 ... read moreMcCullough-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.read less
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