The contact boundary of a complex polynomial (Q1401489)

The authors define the contact boundary of a complex polynomial \(f\colon {\mathbb C}^n\to{\mathbb C}\) as the intersection of some generic fiber with a large sphere and show that, up to contact isotopy, this is independent on the choice of generic fiber. Moreover, it is shown to be invariant under polynomial automorphisms of \({\mathbb C}^n\). It is also shown that the formal homotopy class of the contact structure on the contact boundary does not change under a large class of deformations of the polynomial \(f\), which are not necessarily topologically trivial.