""Contents""; ""Preface""; ""Constructing and deconstructing group actions""; ""On the existence of the self map Ï?92 on the Smith-Toda complex V (1) at the prime 3""; ""1. Introduction and statement of results""; ""2. The Adams spectral sequence of eo2 Î? V(1)""; ""3. Calculation of the Adams E2 term ExtA. (F3, H*(V(1)))""; ""4. The splitting of D(V(1)) Î? V(1)""; ""5. The product rule""; ""6. Selected AHSS calculations of Ï€ * (V (1))""; ""7. The order of the βI action on V(1)""; ""8. Proof that Ï?92 is a permanent cycle""; ""9. Proof that Ï?92 extends over V(1)""; ""References""
""The theory of p-local groups: a survey""""1. The p-completion functor""; ""2. Fusion and linking systems of finite groups""; ""2.1. Fusion systems of groups""; ""2.2. Centric linking systems of groups""; ""2.3. Homotopy Equivalences of p-completed classifying spaces""; ""2.4. Maps from classifying spaces of finite p-groups""; ""2.5. Fusion and linking systems for spaces""; ""2.6. Isotypical equivalences of fusion and linking categories""; ""2.7. Self homotopy equivalences of BGÎ?p""; ""3. The Martino-Priddy conjecture""; ""3.1. Fusion preserving isomorphisms""; ""3.2. Obstruction theory""
3.3. Reduction to simple groups3.4. The odd primary case -- 3.5. Obstruction groups at the prime 2 -- 4. Abstract finite fusion and linking systems -- 4.1. Fusion systems -- 4.2. Centric linking systems -- 4.3. p-local finite groups -- 4.4. Centralizers and mapping spaces -- 4.5. Homology decompositions -- 4.6. Cohomology of the classifying space -- 4.7. Fusion and linking systems determined by their classifying space -- 4.8. Existence and uniqueness of linking systems -- 5. Examples and methods of construction
5.1. Construction of exotic p-local finite groups5.2. Fusion systems of a type studied by Solomon -- 5.3. The fusion system of a block -- 5.4. Extensions of p-local finite groups -- 6. p-local compact groups -- 6.1. Discrete p-toral groups -- 6.2. Fusion and linking systems over discrete p-toral groups -- 6.3. Reduction to finite subcategories -- 6.4. A homology decomposition of the classifying space -- 6.5. Reduced linking systems -- 6.6. Compact Lie groups -- 6.7. p-compact groups -- References -- Fourier decompositions of loop bundles
Weak equivalences of simplicial presheavesKoszul duality of operads and homology of partition posets -- Prologue and introduction -- 0. Conventions -- 1. Composition products and operad structures -- 2. Chain complexes of modules over an operad -- 3. The reduced bar construction -- 4. Bar constructions with coefficients -- 5. Koszul duality for operads -- 6. Epilogue: partition posets -- References -- Glossary and notation index -- On K*(Z) and classical conjectures in the arithmetic of cyclotomic fields -- Finite group actions in elliptic cohomology
Notes
""Topological Hochschild homology and the de Rham-Witt complex for Z(P) -algebras""
