Cover of Book

Lusternik-Schnirelmann Category
ISBN: 0-8218-3404-5


Octav Cornea, Gregory Lupton,
John Oprea and Daniel Tanre

Lusternik-Schnirelmann category is a subject which cuts across the boundary between algebraic topology and dynamical systems. The basic connection between homotopy and dynamics is the LS Theorem that says that the number of critical points of any smooth function on a manifold M is at least as big as the (homotopy invariant) category plus one. Since the time when L and S proved this result, category has expanded enormously in its depth and in its applicability. New applications to symplectic geometry provide even a stronger impetus for studying LS category. The book treats an extensive variety of the many aspects of category from its birth to the present day.

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