De Rham homology for networks of manifolds (Q1083711)

This paper describes the real homology in terms of differential forms for a class of spaces which the author calls networks. The idea is that a network is built up out of pieces which are manifolds and that one describes in a technical way how these pieces are to fit together. As examples one has manifolds, wedges of manifolds, fixed sets of toral actions, classifying spaces of Lie groups (a union of manifolds), simplicial complexes, and more. One of the author's applications is a Thom isomorphism theorem, in which a neighborhood of a network in a manifold is a network formed with tubular neighborhoods of the pieces.