2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78686Recently V. Arnold introduced Strangeness and $J^{\pm}$ invariants of generic immersions of an oriented circle to $\R^2$. Here these invariants are generalized to the case of generic immersions of an oriented circle to an arbitrary surface $F$. We explicitly describe all the invariants satisfying axioms, which naturally generalize the axioms used by V. Arnold.25 pages, 11 figuresGeometric TopologyDifferential Geometry57M99, 57R42 (Primary) 57C42 (Secondary)text