Pairing, Stripes, Lattice Distortions and Superconductivity in Cuprate Oxides

We propose a model for a spatially modulated collective state of superconducting cuprates in which the electronic properties vary locally in space. In this model the regions of higher hole density (called stripes) are described as Luttinger liquids and the regions of lower density (antiferromagnetic ladders) as an interacting bosonic gas of d${}_{x^2-y^2}$ hole pairs. We show that the transition to the superconducting state is topological and driven by decay processes among these elementary excitations in the presence of vibrations.