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Let Gamma ∖ D be an arithmetic quotient of a symmetric space of non-compact type. One can hope to find a Gamma-equivariant deformation retraction of D onto a set D_{0} having dimension equal to the virtural cohomological dimension of Gamma. When such a set exists, it is called a spine and has been studied for many groups. I will first discuss some concrete examples. Then I will describe my thesis work on the existence of spines for Q-rank 1 groups.
Refreshments at 4:00 pm in ES 152