Order one invariants of spherical curves (Q549143)

The author presents a complete description of all order 1 invariants of spherical curves. The study of finite order invariants splits into so called \(J\)-invariants (invariants which are unchanged when passing a triple point) and \(S\)-invariants (invariants which are unchanged when passing a tangency). The author also explicitly identifies the subspaces of all \(J\)-invariants and \(S\)-invariants and presents two inequalities satisfied by any spherical curve. In a previous paper the author has also studied a similar problem for plane curves.