Self-intersection number of immersions and enumeration of nonstable vector bundles

Su-win Yang

Vol. 113 (1984), No. 1, 215–227

DOI: 10.2140/pjm.1984.113.215

Abstract

Suppose N is a closed n-dimensional smooth manifold and M is a 2n-dimensional smooth manifold. In 1944, H. Whitney defined the self-intersection number for an immersion with normal crossings f : N → M. We show that, if N is path-connected and the James-Thomas number of the normal bundle ν(f) of f is greater than 1, then the self-intersection number is completely determined by the homotopy class of f and the normal bundle ν(f).

Mathematical Subject Classification 2000

Primary: 57R42

Secondary: 57R22, 58C27

Milestones

Received: 30 June 1982

Published: 1 July 1984