2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69286We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural subdivision of the Bergman complex of M is a geometric realization of the order complex of its lattice of flats. In addition, we show that the Bergman fan B'(K_n) of the graphical matroid of the complete graph K_n is homeomorphic to the space of phylogenetic trees T_n.15 pages, 6 figures. Reorganized paper and updated references. To appear in J. Combin. Theory Ser. BCombinatorics05B35; 52B05; 92B10text