Gopakumar-Vafa invariants do not determine flops

Understand

Two 3-fold flops are exhibited, both of which have precisely one flopping curve.

• One of the two flops is new, and is distinct from all known algebraic D4-flops.
• It is shown that the two flops are neither algebraically nor analytically isomorphic, yet their curve-counting Gopakumar-Vafa invariants are the same.
• We further show that the contraction algebras associated to both are not isomorphic, so the flops are distinguished at this level.