1981 (Publication #33)
Every Sphere Eversion has a Quadruple Point (with Nelson Max)
View a review of this article at MathSciNet
Let i:S^2 -> R^3 be the inclusion of the sphere, and let X:R^3 -> R^3 be the reflection in the XY plane. An eversion of the sphere is defined to be a regular homotopy of immersions that starts with i and ends with Xi. In this paper, we show that every eversion must have a quadruple point.