Mihai Tibăr

Singularities at infinity and their vanishing cycles

Let f C n C be any polynomial function By using global polar methods we introduce models for the bers of f and we study the monodromy at atypical values of f including the value in nity We construct a geometric monodromy with controlled behavior and de ne global relative monodromy with respect to a general linear form We prove localization results for the relative monodromy and derive a zeta function formula for the monodromy around an atypical value We compute the relative zeta function in several cases and emphasize the di erences to the classical local situation key words topology of polynomial functions singularities at in nity relative monodromy

Real map germs and higher open book structures

The paper focusses on the existence of higher open book structures defined by real map germs \({\psi : (\mathbb{R}^m ,0) \to (\mathbb{R}^p ,0)}\) such that Sing \({\psi \cap \psi^{-1}(0) \subset \{0\}}\). A general existence criterion is proved, with view to weighted-homogeneous maps.The paper focusses on the existence of higher open book structures defined by real map germs

Singular open book structures from real mappings

{\psi : (\mathbb{R}^m ,0) \to (\mathbb{R}^p ,0)}

Global Euler obstruction and polar invariants

such that Sing

Regularity at infinity of real mappings and a Morse–Sard theorem

{\psi \cap \psi^{-1}(0) \subset \{0\}}

Bifurcation values and monodromy of mixed polynomials

. A general existence criterion is proved, with view to weighted-homogeneous maps.