FUNCTIONS AND VECTOR FIELDS ON C(CPn)-SINGULAR MANIFOLDS

Abstract

In this paper we study functions and vector fields with isolated singularities on a C(CPn)-singular manifold. In general, a C(CPn)-singular manifold is obtained from a smooth (2n+1) -manifold with boundary which is a disjoint union of complex projective spaces CPn U center dot center dot center dot UCPn and subsequent capture of the cone over each component CPn of the boundary. We calculate the Euler characteristic of a compact C(CPn)-singular manifold M2n+1 with finite isolated singular points. We also prove a version of the Poincare Hopf Index Theorem for an almost smooth vector field with finite number of zeros on a C(CPn)-singular manifold.