Homotopy groups of generalized {$E(2)$}-local Moore spectra at the prime three
نویسندگان
چکیده
منابع مشابه
Picard Group of the E(2)-local Stable Homotopy Category at the Prime Three
Let L2 denote the stable homotopy category of v−1 2 BP -local spectra at the prime three. In [2], it is shown that the Picard group of L2 consisting of isomorphic classes of invertible spectra is isomorphic to either the direct sum of Z and Z/3 or the direct sum of Z and two copies of Z/3. In this paper, we conclude the Picard group is isomorphic to the latter group by showing the existence of ...
متن کاملOn the homotopy groups of E(n)–local spectra with unusual invariant ideals
Let E(n) and T(m) for nonnegative integers n and m denote the Johnson–Wilson and the Ravenel spectra, respectively. Given a spectrum whose E(n)∗–homology is E(n)∗(T(m))/(v1, . . . , vn−1), then each homotopy group of it estimates the order of each homotopy group of LnT(m). We here study the E(n)–based Adams E2 –term of it and present that the determination of the E2 –term is unexpectedly comple...
متن کاملThe existence of β9t+3 in stable homotopy of spheres at the prime three
Let βs be the generator of the second line of the E2-term of the Adams-Novikov spectral sequence converging to the stable homotopy groups π∗(S) of spheres at the prime three. Ravenel conjectured that the generator βs survives to a homotopy element if and only if s ≡ 0, 1, 2, 3, 5, 6 mod 9. In [9], we proved the ‘only if’ part. In [1], Behrens and Pemmaraju showed that βs survives to a homotopy ...
متن کاملChapter V the Homotopy Groups of H Ring Spectra
This section contains statements of our results on homotopy operations as well as some applications of these results. The proofs depend on material in §2 and will be given in §3Note that, aside from the computations in ~,S at the end of this section, all the results here apply to the homotopy of any H ring spectrum Y. Let ~:DpY + Y denote the structure map. The order of results in this section ...
متن کاملOn the homotopy category of Moore spaces and the cohomology of the category of abelian groups
The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James–Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space. An abelian group A determines the Moore space M(A) = M(A, 2) which up to homotopy equiv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 2005
ISSN: 0018-2079
DOI: 10.32917/hmj/1150922489