Homotopical intersection theory I

Abstract

We give a new approach to intersection theory. Our "cycles" are closed manifolds mapping into compact manifolds and our " intersections" are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn [17], but our proofs are fundamentally different. Errata Minor errors were corrected on page 967 (18 February 2008).