ABSTRACT
In this chapter, we introduce a “nonsingular” version of homotopy, viz., isotopy. In Section 6.1, we discuss the normal bundle and tubular neighborhoods laying down the foundation for homotopical aspects of manifolds. In particular, we prove the existence of “collar neighborhoods” for the boundary a manifold. In Section 6.2, we shall show how vector fields help us to construct isotopies. Isotopies together with collar neighborhoods form an essential part of the tool-kit in differential topology. In section 6.3, we obtain a few ready-to-use results which go a long way in building up new manifolds out of the old. In Section 6.4, we shall see a little bit of ‘smoothing theory’.
