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Abstract

Let T_n be the Teichmuller space of flat metrics on the
n-dimensional torus.  The subspace Y consisting of those points whose
systoles generate the fundamental group of the torus is invariant
for the action of the mapping class group of the torus, SL(n,Z),
and the dimension of Y is equal to the virtual cohomological dimension
of SL(n,Z).  However, we show that Y does not have the same homotopy
type as T_n. This is joint work with Juan Souto.