  Interferometry is a powerful technique used to extract valuable information
about the wave function of a system. In this work, we study the response of
spin carriers to the effective field textures developed in curved
one-dimensional interferometric circuits subject to the joint action of Rashba
and Dresselhaus spin-orbit interactions. By using a quantum network technique,
we establish that the interplay between these two non-Abelian fields and the
circuit's geometry modify the geometrical characteristics of the spinors,
particularly on square circuits, leading to the localisation of the electronic
wave function and the suppression of the quantum conductance. We propose a
topological interpretation by classifying the corresponding spin textures in
terms of winding numbers.
