Advertisement

Lectures on Morse Homology

  • Augustin Banyaga
  • David Hurtubise

Part of the Kluwer Texts in the Mathematical Sciences book series (TMS, volume 29)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Augustin Banyaga, David Hurtubise
    Pages 1-14
  3. Augustin Banyaga, David Hurtubise
    Pages 15-44
  4. Augustin Banyaga, David Hurtubise
    Pages 45-91
  5. Augustin Banyaga, David Hurtubise
    Pages 93-126
  6. Augustin Banyaga, David Hurtubise
    Pages 127-155
  7. Augustin Banyaga, David Hurtubise
    Pages 157-194
  8. Augustin Banyaga, David Hurtubise
    Pages 195-225
  9. Augustin Banyaga, David Hurtubise
    Pages 227-268
  10. Augustin Banyaga, David Hurtubise
    Pages 269-286
  11. Back Matter
    Pages 287-326

About this book

Introduction

This book is based on the lecture notes from a course we taught at Penn State University during the fall of 2002. The main goal of the course was to give a complete and detailed proof of the Morse Homology Theorem (Theo­ rem 7.4) at a level appropriate for second year graduate students. The course was designed for students who had a basic understanding of singular homol­ ogy, CW-complexes, applications of the existence and uniqueness theorem for O.D.E.s to vector fields on smooth Riemannian manifolds, and Sard's Theo­ rem. We would like to thank the following students for their participation in the course and their help proofreading early versions of this manuscript: James Barton, Shantanu Dave, Svetlana Krat, Viet-Trung Luu, and Chris Saunders. We would especially like to thank Chris Saunders for his dedication and en­ thusiasm concerning this project and the many helpful suggestions he made throughout the development of this text. We would also like to thank Bob Wells for sharing with us his extensive knowledge of CW-complexes, Morse theory, and singular homology. Chapters 3 and 6, in particular, benefited significantly from the many insightful conver­ sations we had with Bob Wells concerning a Morse function and its associated CW-complex.

Keywords

Algebraic topology Floer homology Homotopy brandonwiskunde homology homotopy theory manifold

Authors and affiliations

  • Augustin Banyaga
    • 1
  • David Hurtubise
    • 2
  1. 1.The Pennsylvania State UniversityUniversity ParkUSA
  2. 2.The Pennsylvania State UniversityAltoonaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-2696-6
  • Copyright Information Springer Science+Business Media B.V. 2004
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6705-0
  • Online ISBN 978-1-4020-2696-6
  • Series Print ISSN 0927-4529
  • Buy this book on publisher's site