Lusternik-Schnirelmann Category
Author： Octav Cornea;Gregory Lupton;John Oprea
Publisher： American Mathematical Society
Publication year： 2003
E-ISBN: 9781470413309
P-ISBN(Paperback): 9780821834046
P-ISBN(Hardback): 9780821834046
Subject： O189.23 homotopy theory
Keyword： Geometry and Topology
Language： ENG
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Lusternik-Schnirelmann Category
Description
Lusternik-Schnirelmann category is a subject with ties to both algebraic topology and dynamical systems. This book provides a unified approach to LS-category, including foundational material on homotopy theoretic aspects of the subject, 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 which takes LS-category as its central theme and develops topics in topology and dynamics around it. As such, it leads from the very basics of the subject to the present-day state of the art. The prerequisites for reading the book are few: two semesters of algebraic topology and, perhaps, differential topology.