Stratified Morse Theory [Paperback]

Due to the lack of proper bibliographical sources stratification theory seems to be a mysterious subject in contemporary mathematics. This book contains a complete and elementary survey - including an extended bibliography - on stratification theory, including its historical development. Some further important topics in the book are: Morse theory, singularities, transversality theory, complex analytic varieties, Lefschetz theorems, connectivity theorems, intersection homology, complements of affine subspaces and combinatorics. The book is designed for all interested students or professionals in this area.Due to the lack of proper bibliographical sources stratification theory seems to be a mysterious subject in contemporary mathematics. This book contains a complete and elementary survey - including an extended bibliography - on stratification theory, including its historical development. Some further important topics in the book are: Morse theory, singularities, transversality theory, complex analytic varieties, Lefschetz theorems, connectivity theorems, intersection homology, complements of affine subspaces and combinatorics. The book is designed for all interested students or professionals in this area.1. Stratified Morse Theory.- 1.1. Morse-Smale Theory.- 1.2. Morse Theory on Singular Spaces.- 1.3. Two Generalizations of Stratified Morse Theory.- 1.4. What is a Morse Function?.- 1.5. Complex Stratified Morse Theory.- 1.6. Morse Theory and Intersection Homology.- 1.7. Historical Remarks.- 1.8. Remarks on Geometry and Rigor.- 2. The Topology of Complex Analytic Varieties and the Lefschetz Hyperplane Theorem.- 2.1. The Original Lefschetz Hyperplane Theorem.- 2.2. Generalizations Involving Varieties which May be Singular or May Fail to be Closed.- 2.3. Generalizations Involving Large Fibres.- 2.4. Further Generalizations.- 2.5. Lefschetz Theorems for Intersection Homology.- 2.6. Other Connectivity Theorems.- 2.7. The Duality.- 2.8. Historical Remarks.- I. Morse Tl��