We define the (dynamical) core of a topological polynomial (and the
associated lamination). This notion extends that of the core of a unimodal
interval map. Two explicit descriptions of the core are given: one related to
periodic objects and one related to critical objects. We describe all
laminations associated with quadratic and cubic topological polynomials with a
simple core (in the quadratic case, these correspond precisely to points on the
Main Cardioid of the Mandelbrot set).