Alpine Perspectives on Algebraic Topology.

Intro -- Contents -- Preface -- List of Conference Talks -- List of Participants -- L-complete Hopf algebroids and their comodules -- The lattice path operad and Hochschild cochains -- Open-closed field theories, string topology, and Hochschild homology -- Introduction -- 1. Open-closed Topological Field Theories -- 2. The string topology category and its Hochschild homology -- 3. Relations with the Fukaya category of the cotangent bundle -- References -- Cellular covers of divisible abelian groups -- Some geometric properties of the Witten genus -- Localization and cellularization of principal fibrations -- Operadic cobar constructions, cylinder objects and homotopy morphisms of algebras over operads -- Introduction -- The homotopy of operads and of algebras over operads -- 0. The background of dg-modules -- 1. Operads in dg-modules -- 2. The category of algebras associated to an operad -- Applications of the operadic cobar construction -- 3. The operadic cobar construction -- 4. The cobar construction and cofibrant models of algebras over operads -- 5. Cylinder objects and homotopy morphisms -- Bibliography -- Involutions on the rational K-theory of group rings of finite groups -- A quick trip through localization -- 1. Geometric localization -- 2. Geometric localization exists -- 3. Localization of abelian groups -- 4. Classical localization of abelian groups, inverting a set of primes -- 5. Classical localization of spaces -- 6. Limits and derived functors -- 7. Hom and Ext -- 8. p−completion of abelian groups -- 9. p−completion of topological spaces -- 10. Miller's theorem and the Zabrodsky Lemma -- 11. An exotic localization theorem and Serre's theorem -- 12. Applications of exotic localization -- 13. Serre's conjecture -- References -- Divided power structures and chain complexes.

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