Curvature integrals on the real Milnor fibre

  • Nicolas Dutertre

    Université de Provence, Marseille, France

Abstract

Let be a polynomial with an isolated critical point at and let be a one-parameter deformation of . We study the differential geometry of the real Milnor fiber . More precisely, we express the limits

where is the th symmetric function of curvature, in terms of the following averages of topological degrees:

where is the Grassmann manifold of -dimensional planes through the origin of .

When is an algebraically isolated critical point, we study the limits

where the are positive extrinsic curvature functions. We prove that these limits are finite and that they are bounded in terms of the Milnor–Teissier numbers of the complexification of .

Cite this article

Nicolas Dutertre, Curvature integrals on the real Milnor fibre. Comment. Math. Helv. 83 (2008), no. 2, pp. 241–288

DOI 10.4171/CMH/124