Self-intersections of some immersed manifolds

Abstract

The purpose of this paper is to prove a theorem, stated in ?3, which describes the self-intersection manifolds of some immersions of differentiable manifolds in euclidean space in the metastable range. The description is in terms of Z2-bordism, a concept introduced by Conner and Floyd [2] generalizing the cobordism theory of Thom [15]. In ?4 some consequences of the theorem are stated and in ?5 a method is developed for producing immersions of spheres whose self-intersections are the real projective spaces pn for all n. This paper embodies the substance of a thesis submitted to Rice University, written with the advice of Professor Eldon Dyer. During its preparation I was a guest at the City University of New York. I am grateful to Professor John Milnor for his many suggestions.