Detection of a nontrivial element in the stable homotopy groups of spheres

Document Type : Research Paper


South China Normal University


‎Let $p$ be a prime with $p\geq 7$ 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
‎in the Adams spectral sequence where $n\geq 2$ and $3\leq s\leq p-1$‎. 


Main Subjects

Volume 41, Issue 1 - Serial Number 1
February 2015
Pages 65-85
  • Receive Date: 24 September 2013
  • Revise Date: 11 December 2013
  • Accept Date: 12 December 2013
  • First Publish Date: 01 February 2015