Mathematics Colloquia and Seminars

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I will discuss a new type of cohomology, depending on a real parameter q, of a cell complex associated to an infinite Coxeter group W. As q varies these cohomology groups interpolate between ordinary cohomology and cohomology with compact supports. Although these groups are Hilbert spaces (usually infinite dimensional), they can be assigned a "dimension" which is a nonnegative real number. These "dimensions" vary continuously with the parameter q. When q is an integer, they give the L^2 Betti numbers of any regular building of type W and thickness q.