Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The complement of a codimension-k immersion

Michael D. Hirscha1

a1 University of California, Berkeley, CA 94720, U.S.A.

In [1] Marc Feighn proves the following result: a proper, C2, codimension-1 immersion in a manifold with no first homology separates the ambient space. In [4] Michelangelo Vaccaro proves a related result: the C1-immersed image of a compact n-manifold with image a (curved) polyhedron has non-zero Hn with ℤ2 coefficients. (In Vaccaro's terminology f(M) is a curved polyhedron if f is smooth and f(M) is the (non-PL) embedded image of a simplicial complex.) Using ideas similar to Feighn's we prove here the following result.

(Received April 05 1989)

(Revised May 17 1989)