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