Bitangencies on surfaces in four dimensions (Q2730922)

The author proves that given two immersions of closed surfaces \(s:M\to \mathbb R^4\) and \(r:N\to \mathbb R^4\) in general position, one has \(B+D=v(s)v(r)\), where \(D\) is the number of double points counted without sign, \(B\) is the number of bitangencies counted with the sign, and \(v(s)\) is the normal Euler number of \(s\). The author gives a geometric interpretation of the sign of a bitangency, and also gives a geometric interpretation of the correction term in the formula.