Lectures on the h-Cobordism Theorem

by John Milnor

Overview

Important lectures on differential topology by acclaimed mathematician John Milnor

These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnor's goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.

Product Details

ISBN-13:	9780691273730
Publisher:	Princeton University Press
Publication date:	03/25/2025
Series:	Princeton Legacy Library , #2258
Pages:	122
Product dimensions:	6.12(w) x 9.25(h) x (d)

About the Author

John Milnor is one of the most distinguished mathematicians of our time, and has been awarded the Fields Medal, the Wolf Prize, the Abel Prize, and all three Steele prizes. He is a Distinguished Professor of Mathematics at Stony Brook University. He previously taught at Princeton University and was on the faculty of the Institute for Advanced Study in Princeton.

Table of Contents

• Frontmatter, pg. i
• Introduction, pg. iii
• Contents, pg. v
• Section 1. The Cobordism Category, pg. 1
• Section 2. Morse Functions, pg. 7
• Section 3. Elementary Cobordisms, pg. 20
• Section 4. Rearrangement of CobordlBms, pg. 37
• Section 5. A Cancellation Theorem, pg. 45
• Section 6. A Stronger Cancellation Theorem, pg. 67
• Section 7. cancellation of Critical Points in the Middle Dimensions, pg. 85
• Sections 8. Elimination of Critical Points of Index 0 end 1, pg. 100
• Section 9. The h-Cobordism Theorem end Some Applications, pg. 107
• References, pg. 114

Editorial Reviews

John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters

John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society

From the Publisher