Description
This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a class of complexes and featuring matroids as central to the theory. The book illustrates new tools to study the classical theory of matroids as well as their strong geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context; some of the ideas developed raise also new perspectives in the world of matroids. 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 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 topological computations will realize the algorithmic potential of boolean representable complexes.
