Covering the Track of an Isotopy
C. P. Rourke · Proceedings of the American Mathematical Society · 1967
We work in the Polyhedral Category as defined in [3], which consists of polyhedra and polymaps.A polyhedron is a space with a maximal nonempty family of p.l. related triangulations and a polymap is p.l. w.r.t.these triangulations.An ambient isotopy of a polyhedron X is a level-preserving homeo,H: XXI->XXI with H\XXl = l, Ht: X-^X for tEI is the homeo induced by H\XXt.An isotopy of Y in X is a level-preserving embedding, F: YXI-+XXI, Ft: Y-+X for tEI is the embedding induced by p| YXt.We say that H covers F if HtFo=Ft for all tEI, and we say that