... There are corresponding results showing that the Poincare duals of certain totally ge odesic cycles, which we will call "special cycles", span a definite part (a refined Hodge component) of the cohomology of the locally symmetric spaces of standard arithmetic type associated to the orthogonal groups O(p, q). ... Math. ... KLM3] (with B. Leeb and M. Kapovich) The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra, Memoirs of the AMS, Vol. ...