  We use topological methods to study the maximal subgroups of the free
idempotent generated semigroup on a biordered set. We use these to give an
example of a free idempotent generated semigroup with maximal subgroup
isomorphic to the free abelian group of rank 2. This is the first example of a
non-free subgroup of a free idempotent generated semigroup.
