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Free idempotent generated semigroups IG$(E)$, where $E$ is a biordered set,have provided a focus of recent research, the majority of the effortsconcentrating on the behaviour of the maximal subgroups. Inspired by an exampleof Brittenham, Margolis and Meakin, several proofs have been offered that anygroup occurs as a maximal subgroup of some IG$(E)$, the most recent being thatof Dolinka and Ru\v{s}kuc, who show that $E$ can be taken to be a band. From aresult of Easdown, Sapir and Volkov, periodic elements of any IG$(E)$ lie insubgroups. However, little else is known of the `global' properties of IG$(E)$,other than that it need not be regular, even where $E$ is a semilattice.  Since its introduction by Fountain in the late 1970s, the study of abundantand related semigroups has given rise to a deep and fruitful research area. Theclasses of abundant and adequate semigroups extend those of regular and inversesemigroups, respectively, and themselves are contained in the classes of weaklyabundant and weakly adequate semigroups. Recent significant developmentsinclude the description by Kambites, using birooted labelled trees, of the freesemigroups in the quasi-variety of adequate semigroups.  Our main result shows that for any band $B$, the semigroup IG$(B)$ is aweakly abundant semigroup and moreover satisfies a natural condition called thecongruence condition. We show that if $B$ is a band for which $uv=vu=v$ for all$u,v\in B$ with $BvB\subset BuB$ (a condition certainly satisfied forsemilattices), then IG$(B)$ is abundant with solvable word problem. Further,IG$(B)$ is also abundant for a normal band $B$ for which IG$(B)$ satisfies agiven technical condition, and we give examples of such $B$. On the other hand,we give an example of a normal band $B$ such that IG$(B)$ is not abundant.

Free idempotent generated semigroups over bands