Braid Monodromy Type Invariants of Surfaces and 4-Manifolds

In this paper we present the Braid Monodromy Type (BMT) of curves and surfaces. The BMT can distinguish between non-isotopic curves; between different families of surfaces of general type; between connected components of moduli space of surfaces finer than Sieberg-Witten invariants; and between symplectic 4-manifolds.