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Lusternik-Schnirelmann Category and Related Topics
Edited by: O. Cornea, Université de Lille, France, G. Lupton and J. Oprea, Cleveland State University, OH, and D. Tanré, Université de Lille, France
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Contemporary Mathematics
2002; 203 pp; softcover
Volume: 316
ISBN-10: 0-8218-2800-2
ISBN-13: 978-0-8218-2800-7
List Price: US$68
Member Price: US$54.40
Order Code: CONM/316
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This collection is the proceedings volume for the AMS-IMS-SIAM Joint Summer Research Conference, Lusternik-Schnirelmann Category, held in 2001 at Mount Holyoke College in Massachusetts. The conference attracted an international group of 37 participants that included many leading experts. The contributions included here represent some of the field's most able practitioners.

With a surge of recent activity, exciting advances have been made in this field, including the resolution of several long-standing conjectures. Lusternik-Schnirelmann category is a numerical homotopy invariant that also provides a lower bound for the number of critical points of a smooth function on a manifold. The study of this invariant, together with related notions, forms a subject lying on the boundary between homotopy theory and critical point theory.

These articles cover a wide range of topics: from a focus on concrete computations and applications to more abstract extensions of the fundamental ideas. The volume includes a survey article by Peter Hilton that discusses earlier results from homotopy theory that form the basis for more recent work in this area.

In this volume, professional mathematicians in topology and dynamical systems as well as graduate students will catch glimpses of the most recent views of the subject.

Readership

Research mathematicians in topology and dynamical systems and graduate students.

Table of Contents

  • P. Hilton -- Lusternik-Schnirelmann category in homotopy theory
  • M. Arkowitz, D. Stanley, and J. Strom -- The \(\mathcal{A}\)-category and \(\mathcal{A}\)-cone length of a map
  • H. Colman -- Equivariant LS-category for finite group actions
  • H. Colman and S. Hurder -- Tangential LS category and cohomology for foliations
  • M. C. Costoya-Ramos -- Spaces in the Mislin genus of a finite, simply connected co-\(H_{0}\)-space
  • M. Cuvilliez and Y. Félix -- Approximations to the \(\mathcal{F}\)-killing length of a space
  • G. Dula -- Pseudo-comultiplications, their Hopf-type invariant and Lusternik-Schnirelmann category of conic spaces
  • M. Farber -- Lusternik-Schnirelman theory and dynamics
  • C. Gavrila -- The Lusternik-Schnirelmann theorem for the ball category
  • P. Ghienne -- The Lusternik-Schnirelmann category of spaces in the Mislin genus of \(Sp(3)\)
  • J. R. Hubbuck and N. Iwase -- A \(p\)-complete version of the Ganea conjecture for co-\(H\)-spaces
  • G. Lupton -- The rational Toomer invariant and certain elliptic spaces
  • H. J. Marcum -- On the Hopf invariant of the Hopf construction
  • J. Oprea -- Bochner-type theorems for the Gottlieb group and injective toral actions
  • J. Oprea and Y. Rudyak -- Detecting elements and Lusternik-Schnirelmann category of 3-manifolds
  • J. Strom -- Generalizations of category weight
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