The NATO complex learn Institute "Axiomatic, enriched and rna tivic homotopy thought" happened on the Isaac Newton Institute of Mathematical Sciences, Cambridge, England in the course of 9-20 September 2002. the administrators have been J.P.C.Greenlees and I.Zhukov; the opposite or ganizers have been P.G.Goerss, F.Morel, J.F.Jardine and V.P.Snaith. The identify describes the content material good, and either the development and the contents of the current quantity replicate fresh extraordinary successes in version categor ies, dependent ring spectra and homotopy concept of algebraic geometry. The ASI took the shape of a sequence of 15 minicourses and some additional lectures, and was once designed to supply historical past, and to carry the par ticipants modern with advancements. the current quantity is predicated on some of the lectures given in the course of the workshop. The ASI was once the hole workshop of the 4 month programme "New Contexts for reliable Homotopy thought" which explored a number of subject matters in better intensity. i'm thankful to the Isaac Newton Institute for offering such an awesome venue, the NATO technology Committee for his or her investment, and to the entire audio system on the convention, whether they have been in a position to give a contribution to the current quantity. All contributions have been refereed, and that i thank the authors and referees for his or her efforts to slot in with the tight agenda. eventually, i want to thank my coorganizers and all of the employees on the Institute for making the ASI run so easily. J.P.C.GREENLEES.
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