This self-contained monograph explores a new theory centered around boolean representations of
simplicial complexes leading to a new class of complexes featuring matroids as central to the
theory. The book illustrates these new tools to study the classical theory of matroids as well
as their important geometric connections. Moreover many geometric and topological features of
the theory of matroids find their counterparts in this extended context.Graduate students and
researchers working in the areas of combinatorics geometry topology algebra and lattice
theory will find this monograph appealing due to the wide range of new problems raised by the
theory. Combinatorialists will find this extension of the theory of matroids useful as it opens
new lines of research within and beyond matroids. The geometric features and geometric
topological applications will appeal to geometers. Topologists who desire to perform algebraic
topology computations will appreciate the algorithmic potential of boolean representable
complexes.
