On geometrically finite degenerations I: boundaries of main hyperbolic components

We develop a theory of quasi post-critically finite degenerations Blaschke products. This gives us tools to study the boundaries hyperbolic components rational maps in higher-dimensional moduli spaces. use it obtain combinatorial classification geometrically polynomials on boundary main component $\mathcal{H}\_d$, i.e., space monic and centered that contains $z^d$. also show closure $\overline{\mathcal{H}\_d}$ is not topological manifold with for $d\geq 4$ by constructing self-bumps its boundary.