Stratified Morse Theory

by Mark Goresky, Robert MacPherson

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 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.

Hardcover

First published March 21, 1988

Reviews

[Andrew]

No doubt it is a very important text and has excellent ideas. It also has a nice introduction. The technique of "moving the wall" and those lemmas about fringed sets and characteristic covectors seem to really speak to the difficulties of conveying geometric intuition. They're really difficult to read (personally, I skipped these sections). If you pick this book up, make sure not to skip the heart of part III: the perfection of the Morse function.