Boolean Representations of Simplicial Complexes and Matroids, Softcover reprint of the original 1st ed. 2015 Springer Monographs in Mathematics Series

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.

Contains open problems and new ideas for research

Develops a geometric theory in an extended context

Uses the lattice structure for all representations of boolean representations of simplicial complexes

Includes supplementary material: sn.pub/extras