An Introduction to Intersection Homology Theory, Second Edition [Hardcover]

Frances Kirwan (Author), Jonathan Woolf (Author)

Book Description

ISBN-10: 1584881844 | ISBN-13: 978-1584881841 | Publication Date: June 7, 2006 | Edition: 2

Now more that a quarter of a century old, intersection homology theory has proven to be a powerful tool in the study of the topology of singular spaces, with deep links to many other areas of mathematics, including combinatorics, differential equations, group representations, and number theory.

Like its predecessor, An Introduction to Intersection Homology Theory, Second Edition introduces the power and beauty of intersection homology, explaining the main ideas and omitting, or merely sketching, the difficult proofs. It treats both the basics of the subject and a wide range of applications, providing lucid overviews of highly technical areas that make the subject accessible and prepare readers for more advanced work in the area. This second edition contains entirely new chapters introducing the theory of Witt spaces, perverse sheaves, and the combinatorial intersection cohomology of fans.

Intersection homology is a large and growing subject that touches on many aspects of topology, geometry, and algebra. With its clear explanations of the main ideas, this book builds the confidence needed to tackle more specialist, technical texts and provides a framework within which to place them.

Product Details

• Hardcover: 248 pages
• Publisher: Chapman and Hall/CRC; 2 edition (June 7, 2006)
• Language: English
• ISBN-10: 1584881844
• ISBN-13: 978-1584881841
• Product Dimensions: 9.3 x 6.2 x 0.9 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #521,226 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

3.0 out of 5 stars good content and style, but crippling number of typos, August 10, 2009

By 

Sean Rostami (Maryland, USA) - See all my reviews

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This review is from: An Introduction to Intersection Homology Theory, Second Edition (Hardcover)

This book is a very enjoyable survey of intersection (co)homology. It first introduces multiple (co)homology theories and states and/or proves the "de Rham" theorems for pairs of them. It then introduces "stratified spaces" and intersection (co)homology. There are lots of hands-on computations to look at, similar in flavor to the CW-complex problems from your algebraic topology class. There's some abstract derived category stuff with a few pages on Verdier duality. It also discusses Deligne's axiomatic characterization (within the derived category) of the intersection sheaf complex. There's lots of other stuff in it that I haven't read (despite the fact that it's only 200 pages).

HOWEVER, the number of typos is enormous. Most of them are obviously the fault of the publisher, not the authors (for instance, the letter 'f' replacing '...' in a filtration). It's really hard to read sometimes. Indices are screwed up or suppressed (which is pretty F%&*$ relevant when you're trying to learn what a perverse sheaf is...). Maybe they fixed these in a later printing, but you've been warned.

I actually wanted to give it 4 stars, but I felt that would reduce the impact of the typo complaint.

Edit: I just noticed that my tag of "perverse sheaves" refuses to show
up, even if I say "_perverse" or "-perverse" or whatever. What is
this, North Korea? There are objects in mathematics called "perverse
sheaves". The name is bad for a few reasons, but that's what they're
called. People need to be able to search for it. Other books have this phrase in their titles. What's the big deal? PERVERSE PERVERSE PERVERSE! You can buy pr0n on Amazon, so stop pretending.