On higher dimensional light bulb theorem
Yoshihiko Marumoto · Institutional Repositories DataBase (IRDB) · 1986
It is well known that any two arcs with the same end points in R 3 or S 3 can be moved isotopically from one to the other keeping the end points fixed during the deformation.This is called Light Bulb Theorem ([8]).In this paper, we prove the Light Bulb Theorem is valid in the higher dimensional case.As an application, we will give a characterization of invertible knots concerning with J. M. Montesinos' question ([4]).Throughout the paper, we work in the piecewise linear category.For an oriented manifold X, by -X we mean the manifold with the opposite orientation, and for oriented manifolds X and Y, X = Y means that X = Y as point sets and that the orientations of X and Y coincide.In this paper, every submanifold in a manifold is assumed to be locally fiat.A ball pair (B", Bm) is unknotted if it is homeomorphic to (Bm x [ -1, 1Jn-m, Bm x (0, ... , 0)) as a pair.A sphere pair (S", Sm) is unknotted if Sm bounds an (m + 1)-disk in S".