  Topological defects determine the collective properties of anisotropic
materials. How their configurations are controlled is not well understood
however, especially in 3D, where bulk-surface coupling can render the geometry
of confining boundaries relevant. This is particularly important in living
matter, where 2D topological defects have been linked to essential biological
functions, whereas the role of 3D defects is unclear. Motivated by
multicellular systems interacting with extracellular boundaries, we consider a
polar fluid confined within curved boundaries imposing weak surface anchoring.
We report a novel charge-preserving transition between different defect
configurations, controlled by the boundary shape, and invariant to changes in
the material parameters. We test if this geometry-driven transition occurs in
confined multicellular systems and investigate the biological role of 3D polar
defects in the mouse epiblast -- an embryonic tissue consisting of
apico-basally polarised cells. We find that fluid-filled lumina -- structures
essential for subsequent embryonic development -- tend to form near defect
positions of polar fluids in embryo-like confinement geometries. Moreover, by
experimentally perturbing embryo shape beyond the transition point, we trigger
the formation of additional lumen nucleation sites at the predicted position.
Thus, our work reveals how boundary geometry controls polar defects, and how
embryos use this mechanism for shape-dependent lumen formation. Because this
defect control principle is independent of specific material properties, we
expect it to apply universally to systems with orientational order.
