  We describe a topological protection mechanism for highly-twisted
two-dimensional Skyrmions in systems with Dyloshinskii-Moriya (DM) coupling,
where non-zero DM energy density (dubbed "twisting energy density") acts as a
kind of band gap in real space, yielding an N invariant for highly twisted
Skyrmions. We prove our result through the application of contact topology by
extending our system along a fictitious third dimension, and further establish
the structural stability of highly-twisted Skyrmions under arbitrary
chirality-preserving distortions. Our results apply for all two-dimensional
systems hosting Skyrmion excitations including spin-orbit coupled systems
exhibiting quantum Hall ferromagnetism.
