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Lusternik-Schnirelmann Category
Octav Cornea, Université de Montreal, QC, Canada, Gregory Lupton and John Oprea, Cleveland State University, OH, and Daniel Tanré, Université de Lille, France
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Mathematical Surveys and Monographs
2003; 330 pp; hardcover
Volume: 103
ISBN-10: 0-8218-3404-5
ISBN-13: 978-0-8218-3404-6
List Price: US$92
Member Price: US$73.60
Order Code: SURV/103
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"Lusternik-Schnirelmann category is like a Picasso painting. Looking at category from different perspectives produces completely different impressions of category's beauty and applicability."

--from the Introduction

Lusternik-Schnirelmann category is a subject with ties to both algebraic topology and dynamical systems. The authors take LS-category as the central theme, and then develop topics in topology and dynamics around it. Included are exercises and many examples. The book presents the material in a rich, expository style.

The book provides a unified approach to LS-category, including foundational material on homotopy theoretic aspects, the Lusternik-Schnirelmann theorem on critical points, and more advanced topics such as Hopf invariants, the construction of functions with few critical points, connections with symplectic geometry, the complexity of algorithms, and category of \(3\)-manifolds.

This is the first book to synthesize these topics. It takes readers from the very basics of the subject to the state of the art. Prerequisites are few: two semesters of algebraic topology and, perhaps, differential topology. It is suitable for graduate students and researchers interested in algebraic topology and dynamical systems.

Readership

Graduate students and research mathematicians interested in algebraic topology and dynamical systems.

Reviews

"Finally! The book that sums up the explosive development of the Ljusternik-Schnirelman theory in the past decade has now appeared."

-- Zentralblatt MATH

"A carefully written, well-conceived and timely addition to the literature on category ... copious references, many interesting exercises and two helpful appendices ... should prove invaluable both as a reference for experts and as a text for a graduate seminar."

-- Mathematical Reviews

Table of Contents

  • Introduction to LS-category
  • Lower bounds for LS-category
  • Upper bounds for category
  • Localization and category
  • Rational homotopy and category
  • Hopf invariants
  • Category and critical points
  • Category and symplectic topology
  • Examples, computations and extensions
  • Topology and analysis
  • Basic homotopy
  • Bibliography
  • Index
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