Abstract: CAT(0) spaces are spaces that model non-negatively curved behavior, and CAT(0) groups are those that act on such spaces in a sufficiently nice way. The CAT(0) property is not known to be preserved by abstract commensurability. Right-angled Coxeter groups (RACGs) are an important class of examples with a variety of nice geometric, algebraic and algorithmic properties. I'll discuss joint work with Charles Cunningham, Adam Piggott, and Kim Ruane in which we show that certain split extensions of RACGs are CAT(0), but for very different reasons depending on the type of extension. Time permitting, I'll mention some interesting extensions for which the CAT(0) property has not been proved or disproved. This talk will be entirely accessible for grad students; I'll give all necessary background.
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