Perspectives on A-homotopy theory and its applications

This paper contains a survey of the A-theory of simplicial complexes and graphs, a combinatorial homotopy theory developed recently. The initial motivation arises from the use of simplicial complexes as models for a variety of complex systems and their dynamics. This theory diverges from classical homotopy theory in several crucial aspects. It is related to prior work in matroid theory, graph theory, and work on subspace arrangements.