  This paper provides a complete classification of torus-invariant curves in
Cherkis bow varieties of type A. We develop combinatorial codes for compact and
noncompact invariant curves involving the butterfly diagrams, Young diagrams,
and binary contingency tables. As a key intermediate step, we also develop a
novel tangent weight formula. Finally, we apply this new machinery to example
bow varieties to demonstrate how to obtain their 1-skeletons (union of fixed
points and invariant curves).
