THE HOMOTOPY GROUPS OF SE(2) AT p ≥ 5 REVISITED
نویسنده
چکیده
We present a new technique for analyzing the v0-Bockstein spectral sequence studied by Shimomura and Yabe. Employing this technique, we derive a conceptually simpler presentation of the homotopy groups of the E(2)-local sphere at primes p ≥ 5. We identify and correct some errors in the original ShimomuraYabe calculation. We deduce the related K(2)-local homotopy groups, and discuss their manifestation of Gross-Hopkins duality.
منابع مشابه
ar X iv : 0 70 9 . 39 25 v 1 [ m at h . A T ] 2 5 Se p 20 07 HOMOTOPY NILPOTENT GROUPS
We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove, that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups. Finally ...
متن کاملA new family in the stable homotopy groups of spheres
Let $p$ be a prime number greater than three. In this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(S)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm Ext}_A^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ up to nonzero scalar in the Adams spectral sequence, where $ngeq m+2>5$, $0leq sExt}_A^{s+2,q[(s+2)p...
متن کاملDetection of a nontrivial element in the stable homotopy groups of spheres
Let $p$ be a prime with $pgeq 7$ and $q=2(p-1)$. In this paper we prove the existence of a nontrivial product of filtration $s+4$ in the stable homotopy groups of spheres. This nontrivial product is shown to be represented up to a nonzero scalar by the product element $widetilde{gamma}_{s}b_{n-1}g_{0}in {Ext}_{mathcal{A}}^{s+4,(p^n+sp^2+sp+s)q+s-3}(mathbb{Z}/p,mathbb{Z}/p)$ in ...
متن کاملThe Wirthmüller Isomorphism Revisited
We show how the formal Wirthmüller isomorphism theorem proven in [2] simplifies the proof of the Wirthmüller isomorphism in equivariant stable homotopy theory. Other examples from equivariant stable homotopy theory show that the hypotheses of the formal Wirthmüller and formal Grothendieck isomorphism theorems in [2] cannot be weakened.
متن کاملOn the Nilpotence Order of β 1
For p > 2, β1 ∈ π 2p2−2p−2(S) is the first positive even-dimensional element in the stable homotopy groups of spheres. A classical theorem of Nishida [Nis73] states that all elements of positive dimension in the stable homotopy groups of spheres are nilpotent. In fact, Toda [Tod68] proved β 2−p+1 1 = 0. For p = 3 he showed that β 1 = 0 while β 5 1 6= 0. In [Rav86] the second author computed the...
متن کامل