## Mumford's 2-dimensional complex and generalizations

#### Ron LivneHebrew University, Jerusalem, IsraelMathematics

In 1979 Mumford constructed a lattice in PGL(3) over the
2-adic numbers with particularly nice properties. The
associated quotient of the building is a "very small"
complex. We give a finite and simple description
of this complex, which hinges on the isomorphism of
GL(3,F_2) with PSL(2,F_7). We use it to compute a
presentation for the lattice, and give a generalization
of our construction to complexes associated to PSL(2,F_q).

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