  Three-dimensional $\mathcal{N} = 4$ superconformal field theories contain 1d
topological sectors consisting of twisted linear combinations of half-BPS local
operators that can be inserted anywhere along a line. After a conformal mapping
to a round three-sphere, the 1d sectors are now defined on a great circle of
$S^3$. We show that the 1d topological sectors are preserved under the
squashing of the sphere. For gauge theories with matter hypermultiplets, we use
supersymmetric localization to derive an explicit description of the
topological sector associated with the Higgs branch. Furthermore, we find that
the dependence of the 1d correlation functions on the squashing parameter $b$
can be removed after appropriate rescalings. One can introduce real mass and
Fayet-Iliopolous parameters that, after appropriate rescalings, modify the 1d
theory on the squashed sphere precisely as they do on the round sphere. In
addition, we also show that when a generic 3d $\mathcal{N}=4$ theory is
deformed by real mass parameters, this deformation translates into a universal
deformation of the corresponding 1d theory.
