A geometric study of certain stochastic semigroups

An affine topological semigroup is a convex subset S of a real topological vector space, together with a continuous associative multiplication which is also an affine function on each of its two variables. For each idempotent E in the affine semigroup of stochastic matrices Sn, the following two compact affine subsemigroups are studied: the maximal monoid in Sn with identity E, denoted by ESnE; and the core of E in Sn, denoted by Q(E), which is the maximal subsemigroup of Sn with zero element E. [...]