The Topology of Complex Analytic Varieties and the Lefschetz Hyperplane Theorem

One of the main sets of mathematical results proved in this book is a collection of theorems on the topology of complex analytic varieties. There are generalizations of the Lefschetz hyperplane theorem for complex projective varieties, and generalizations of the theorem that the homotopy dimension of a Stein manifold is bounded by its complex dimension. In this section of the introduction, we give a sketch of the statements of the theorems with motivation and some history. Technically precise statements of the theorems in their most general form are grouped together in Chapter 1 of Part II of the book.