Titlebook: Cohomological Methods in Homotopy Theory; Barcelona Conference Jaume Aguadé,Carles Broto,Carles Casacuberta Conference proceedings 2001 Bir

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Composition methods in the homotopy groups of ring spectra,plies that for certain spaces, the unstable homotopy is as accessible as the stable homotopy. It is the purpose of this work to examine how, in certain cases, the methods of Toda can be used for spaces other than spheres. We will begin by summarizing the methods used by Toda. We will discuss the pos

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New relationships among loopspaces, symmetric products, and Eilenberg Maclane spaces,s of .’s corresponding to the wedge occurring in the . = 1 case above..One can also map the .(., .) to each other as . varies, and here the cohomological calculations imply a homotopical conclusion: the hocolimits that are nonzero, .(∞, 2.), for . ≥ 0, map to each other, giving rise to a fitration o

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Stripping and splitting decorated mapping class groups,stabilization maps with respect to the genus, the number of punctures and boundary components. Decorated mapping class groups are non-trivial extensions of the undecorated mapping class group, and the first result states that the extension is homologically trivial when one stabilizes with respect to

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Composition methods in the homotopy groups of ring spectra,ich the EHP sequences of James and Whitehead were used inductively; “composition methods” were used to construct elements and evaluate homomorphisms. The second was the Adams spectral sequence. Each method has advantages and disadvantages. Toda’s method has the advantage that unstable homotopy group

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Tate cohomology in axiomatic stable homotopy theory,e ho-motopy theory of Hovey—Palmieri—Strickland [32]. Much of the work consists of collecting known results in a single language and a single framework. The very effortlessness of the process is an effective advertisement for the language, and a call for further investigation of other instances. The