  Local models are schemes, defined in terms of linear algebra, that were
introduced by Rapoport and Zink to study the \'etale-local structure of
integral models of certain PEL Shimura varieties over p-adic fields. A basic
requirement for the integral models, or equivalently for the local models, is
that they be flat. In the case of local models for even orthogonal groups,
Genestier observed that the original definition of the local model does not
yield a flat scheme. In a recent article, Pappas and Rapoport introduced a new
condition to the moduli problem defining the local model, the so-called spin
condition, and conjectured that the resulting "spin" local model is flat. We
prove a weak form of their conjecture in the split, Iwahori case, namely that
the spin local model is topologically flat. An essential combinatorial
ingredient is the equivalence of mu-admissibility and mu-permissibility for two
minuscule cocharacters mu in root systems of type D.
