Mathematics – Algebraic Topology
Scientific paper
2009-11-06
Chin. Ann. Math. Ser. B 29 (3) (2008), 291-316
Mathematics
Algebraic Topology
19 pages
Scientific paper
In this paper we constructs a new nontrivial family in the stable homotopy groups of spheres $\pi_{p^nq+2pq+q-3}S$ which is of order $p$ and is represented by $k_0h_{n} \in Ext_A^{3,p^nq+2pq+q}(\mathbb{Z}_p,\mathbb{Z}_p)$ in the Adams spectral sequence, where $p\geq 5$ is an odd prime, $n\geq 3$ and $q=2(p-1)$. In the course of the proof, a new family of homotopy elements in $\pi_{\ast}V(1)$ which is represented by $\beta_{\ast}{i^{\prime}}_{\ast}i_{\ast}({h}_n)\in Ext_A^{2,p^nq+(p+1)q+1}(H^{\ast}V(1),\mathbb{Z}_p)$ in the Adams sequence is detected.
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