Intersection-complexes. I. Combinatory Theory
M. H. A. Newman · Mathematical Proceedings of the Cambridge Philosophical Society · 1931
The theory of the intersection-complex Ch · Ck, due originally to Veblen, Weyl, Alexander and Lefschetz, has recently been extended by Flexner to cover intersections on a “topological n-manifold” (locally Cartesian n-space) in the case h + k = n. In his theory the whole of Lefschetz's work for ordinary simplicial manifolds is presupposed, including the rather difficult approximations. The object of the present paper is to provide a combinatory theory of the general intersection, (h + k ≥ n), which would serve equally well as a basis for Flexner's work, and avoids the wasteful process of using two independent approximations.