(Slide 3)

The basic data types in Chains include 1) standard programming language constructs such as scalars and vectors, 2) algebraic objects such as groups, rings, and fields, 3) discrete topological objects, such as vertices, cells, and cell complexes, 4) algebraic-topological chains and cochains, which are the link between the algebraic and topological worlds, and 5) operations on chains and cochains, including the skew-symmetric linear algebraic-topological operators boundary and coboundary.