  We describe the geometry of bend distortions in twist-bend nematic liquid
crystals in terms of their fundamental degeneracies, which we call $\beta$
lines. These represent a new class of line-like topological defect. We use them
to construct and characterise novel structures, including grain boundary and
focal conic smectic-like defects, Skyrmions, and knotted merons. We analyse
their local geometry and global structure, showing that their intersection with
any surface is twice the Skyrmion number. Finally, we demonstrate how arbitrary
knots and links can be created and describe them in terms of merons, giving a
new geometric perspective on the fractionalisation of Skyrmions.
