Counting indices of critical points of rank two of polynomial selfmaps of R4

Abstract

For a generic f ∈ C ∞ (R 4 , R 4 ) there is a discrete set Σ 2 (Df ) of critical points of rank two, and there is an integer index I p (Df ) associated to any p ∈ Σ 2 (Df ). We show how to compute I p (Df ), p ∈ Σ 2 (Df ), in the case where f is a polynomial mapping.