Lusternik-Schnirelmann Category and Related Topics
About this Title
O. Cornea, G. Lupton, J. Oprea and D. Tanré, Editors
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 and its contributions here represent an international group of the leading practitioners in the field.
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 for research mathematicians and graduate students. Some focus on concrete computations and applications while others look at more abstract extensions of the fundamental ideas.
Research mathematicians in topology and dynamical systems and graduate students.
Table of Contents
- Peter Hilton – Lusternik-Schnirelmann category in homotopy theory [MR 1962149]
- Martin Arkowitz, Donald Stanley and Jeffrey Strom – The $\scr A$-category and $\scr A$-cone length of a map [MR 1962150]
- Hellen Colman – Equivariant LS-category for finite group actions [MR 1962151]
- Hellen Colman and Steven Hurder – Tangential LS category and cohomology for foliations [MR 1962152]
- M. Cristina Costoya-Ramos – Spaces in the Mislin genus of a finite, simply connected co-$H_0$-space [MR 1962153]
- M. Cuvilliez and Y. Félix – Approximations to the $\scr F$-killing length of a space [MR 1962154]
- Giora Dula – Pseudo-comultiplications, their Hopf-type invariant and Lusternik-Schnirelmann category of conic spaces [MR 1962155]
- Michael Farber – Lusternik-Schnirelman theory and dynamics [MR 1962156]
- Caius Gavrila – The Lusternik-Schnirelmann theorem for the ball category [MR 1962157]
- Pierre Ghienne – The Lusternik-Schnirelmann category of spaces in the Mislin genus of $\rm Sp(3)$ [MR 1962158]
- J. R. Hubbuck and Norio Iwase – A $p$-complete version of the Ganea conjecture for co-$H$-spaces [MR 1962159]
- Gregory Lupton – The rational Toomer invariant and certain elliptic spaces [MR 1962160]
- Howard J. Marcum – On the Hopf invariant of the Hopf construction [MR 1962161]
- John Oprea – Bochner-type theorems for the Gottlieb group and injective toral actions [MR 1962162]
- John Oprea and Yuli Rudyak – Detecting elements and Lusternik-Schnirelmann category of 3-manifolds [MR 1962163]
- Jeffrey Strom – Generalizations of category weight [MR 1962164]