J P C Greenlees

Axiomatic, Enriched and Motivic Homotopy Theory: Proceedings of the NATO Advanced Study Institute on Axiomatic, Enriched and Motivic Homotopy Theory Cambridge, United Kingdom 9-20 September 2002 - NATO Science Series II J P C Greenlees 2004 edition

Marc Notes: Avail. in paper (ISBN 1402018347) at EUR 65.00; Includes bibliographical references. Table of Contents: Contributing Authors. Preface. Part I: General surveys. Localizations; W. G. Dwyer. 1. Introduction. 2. Algebra. 3. Homological localization in topology. 4. Localization with respect to a map. 5. Colocalization with respect to an object. 6. Higher invariants of localization. 7. Constructing localizations and colocalizations. References. Generalized sheaf cohomology theories; J. F. Jardine. 1. Simplicial presheaves. 2. Presheaves of spectra. 3. Profinite groups. 4. Generalized Galois cohomology theory. 5. Thomason's descent theorem. References. Axiomatic stable homotopy; N. P. Strickland. 1. Introduction. 2. Axioms. 3. Functors on small objects. 4. Types of subcategories. 5. Quotient categories and Blousfield localization. 6. Versions of the Blousfield lattice. 7. Special types of localization. 8. Nilpotence. 9. Brown representability. References. Part II: Special surveys. (Pre-)sheaves of ring spectra; P. C. Goerss. 1. The realization problem. 2. Moduli spaces and obstruction theory. References. Operads and cosimplicial objects: an introduction; J. E. McClure, J. H. Smith. 1. Introduction. 2. Loop lattices and the little intervals operad. 3. Cosimplicial objects and totalization. 4. A sufficient condition for Tot(X.) to be an AINFINITY space. 5. A reformulation. 6. Operads. 7. A family of cochain operations.8. A sufficient condition for Tot(X ) to be an E8 space. 9. The little n-cubes operad. 10. A sufficient condition for Tot(X ) to be an En space. 11. An extension of Remark 6.3(b). 12. Proof of Theorem 10.6. 13. Applications. 14. The framed little disks operad. 15. Cosimplicial chain complexes. 16. Applications. References. From HAG to DAG: derived moduli stacks; B. Toen, G. Vezzosi. 1. Introduction. 2. The model category of D-stacks. 3. First examples of D stacks. 4. The geometry of D-stacks. 5. Further examples. References. Part III: Motivic homotopy theory. On the motivic &pgr;0 of the sphere spectrum; F. Morel. 1. Introduction. 2. From smooth varieties to 'spaces'. 3. Stable homotopy categories of S1-spectra. 4. The &mathA;1-homotopy t-structure and the stable Hurewicz theorem. 5. Inverting &mathP;1. &pgr;0(S0) and Milnor-Witt K theory of fields. References. Riemann-Roch Theorems for oriented cohomology; I. Panin (after I. Panin, A. Smirnov). 0. Introduction. 1. Oriented cohomology pretheories. 2. Riemann-Roch type theorems. References. Equivariant motivic phenomena; V. Snaith. 1. Introduction. 2. Classical motives. 3. Equivariant Motives. 4. The Gross-Stark conjecture. 5. The fractional ideal"Publisher Marketing: This book consists of a series of expository articles on axiomatic, enriched and motivic homotopy theory arising out of a NATO Advanced Study Institute of the same name at the Isaac Newton Institute for the Mathematical Sciences in Cambridge, UK in September 2002. There are introductions to abstract, stable and enriched homotopy theory, motivic homotopy categories, and stacks. Articles include applications to stable homotopy theory, higher commutativity, K-theory and descent. The list of authors brings together experts from both the homotopy theoretic and motivic sides, bridging the cultural divide between them.