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Let T_n be the Teichmueller space of flat metrics on the n-dimensional torusand identify SL(n,Z) with the corresponding mapping class group. We prove thatthe subset Y consisting of those points at which the systoles generate thefundamental group of the torus is, for n > 4, not contractible. In particular,Y is not an SL(n,Z)-equivariant deformation retract of T_n.

The spine which was no spine