MAYER-VIETORIS PROPERTY OF THE FIXED POINT INDEX

We study a Mayer-Vietoris kind formula for the fixed point index of maps of ENR triplets f : (X; X-1, X-2) -> (X; X-1, X-2) having compact fixed point set. We prove it under some suitable conditions. For instance when (X; X-1, X-2) = (E-n; E-+(n), E--(n)). We use these results to generalize the Poincare-Bendixson index formula for vector fields to continuous maps having a sectorial decomposition, to study the fixed point index i(f, 0) of orientation preserving homeomorphisms of E-+(2) and (E-3; E-+(3), E--(3)) and the fixed point index in the invariant subspace.