Foundations of a connectivity theory for simplicial complexes

This paper lays the foundations of a combinatorial homotopy theory, called A-theory, for simplicial complexes, which reflects their connectivity prope rties. A collection of bigraded groups is constructed, and methods for comp utation are given. A Seifert-Van Kampen type theorem and a long exact seque nce of relative A-groups are derived. A related theory for graphs is constr ucted as well. This theory provides a general framework encompassing homoto py methods used to prove connectivity results about buildings, graphs, and matroids. (C) 2001 Academic Press.