Manuel Gonzalez Villa, CIMAT: On a Quadratic Form Associated with a Surface Automorphism and its Applications to Singularity Theory
We study the nilpotent part N of a pseudo-periodic automorphism h of a real oriented surface with boundary Σ. We associate a quadratic form Q defined on the first homology group (relative to the boundary) of the surface Σ. Using the twist formula and techniques from mapping class group theory, we prove that after killing ker N the form becomes positive definite if all the screw numbers associated with certain orbits of annuli are positive. The case of monodromy automorphisms of Milnor fibers Σ = F of germs of curves on normal surface singularities will be discussed in detail.
