Presented By: Topology Seminar  Department of Mathematics
Topology Seminar: A SolomonTits Theorem for Rings
Matthew Scalamandre (Notre Dame)
The classical Solomon–Tits theorem states that a spherical Tits building over a field is homotopy equivalent to a wedge of spheres of the appropriate dimension. In this talk, we’ll define a Tits complex that makes sense for an arbitrary ring, and prove a SolomonTits theorem when R either satisfies a stable range condition, or is the ring of Sintegers of a number field. We will discuss applications to the cohomology of principal congruence subgroups of SL_n(Z), and some results about the top homology of this complex (an analogue of the classical Steinberg representation).
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