Pairs of Polyhedra and Isotopies

Abstract

In this chapter we recast the last two chapters for pairs of polyhedra and manifolds. The proofs of the extended results will often be essentially the same as those of the original results and in this case we will refer back and merely sketch the changes; if the changes are obvious the proof will be omitted. We give two applications to isotopies. The first concerns “cellular moves” and will be used in the next chapter to prove basic unknotting theorems. The second application is to the general isotopy extension theorem, and is given in the final section of the chapter; this theorem will not be used again in the book and this section may be omitted or read at any later stage if the reader wishes.