Normally branched line fields on odd-dimensional manifolds

Abstract

A Poincare-Hopf theorem relating the branching and the point defects of a regularly defect tangential line field to the Euler characteristic is well-known for even-dimensional manifolds. We prove such a theorem in the normally branched case for odd-dimensional boundaries and apply it to boundary problems associated with isolated singularities of complex hypersurfaces. (C) 2002 Elsevier Science B.V. All rights reserved.