منابع مشابه
Duality and Eilenberg - Mac Lane Spectra
Stable cohomotopy groups of Eilenberg-Mac Lane spectra of finite groups are shown to be trivial. This implies that the stable homotopy category, which is large enough to represent ordinary cohomology theory, cannot be self-dual. It can also be interpreted as an evidence to support Freyd's generating hypothesis and a proof of a stable version of a conjecture of D. Sullivan.
متن کاملHomological Localizations of Eilenberg-mac Lane Spectra
We discuss the Bousfield localization LEX for any spectrum E and any HR-module X, where R is a ring with unit. Due to the splitting property of HR-modules, it is enough to study the localization of Eilenberg– MacLane spectra. Using general results about stable f -localizations, we give a method to compute the localization of an Eilenberg–MacLane spectrum LEHG for any spectrum E and any abelian ...
متن کاملGroups with finite 2-dimensional Eilenberg–Mac Lane spaces
This theorem seems to come tantalizingly close to supplying counter-examples to the Eilenberg–Ganea conjecture, which asserts that any group of cohomological dimension 2 admits a (not necessarily finite) 2-dimensional Eilenberg–Mac Lane space. Indeed, I don’t know of any example of a finitely-presented group with an infinite 2-dimensional K(Γ, 1) but not a finite one, but such things surely exi...
متن کاملMorava K -theory of Eilenberg-mac Lane Spaces
This talk is about a 1980s computation by Ravenel and Wilson of the Morava K -theories of certain EilenbergMac Lane spaces. This is a really neat computation, and it involves essentially all the sorts of algebra and algebraic geometry we have at our disposal, and it highlights how K -theory can serve as a conduit for them. The paper on which this talk is based is nearly 60 pages long, and the e...
متن کاملRegs Report: the Morava E-theory of Eilenberg-mac Lane Spaces
These properties fuel many arguments involving the decomposition of spaces, where more complex homology theories would instead have nontrivial spectral sequences obstructing similar results. In the 1960s, Ravenel and Wilson [8] computed K(n)∗K(Z, q) for all n and q, using the Künneth isomorphism to show that the functor K(n)∗ took the ring object K(Z, ∗) to a π∗K(n)-coalgebraic ring K(n)∗K(Z, ∗...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.2307/2038905