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

Zhong, Linan¹ ; Wang, Yuyu²

¹Department of Mathematics, Yanbian University, No. 977, Gong Yuan Road, Yanji 133000, China, and, School of Mathematical Sciences, Nankai University, Tianjin 300071, China
²College of Mathematical Science, Tianjin Normal University, No.393, Extension of Bin Shui West Road, Xi Qing District, Tianjin 300387, China

Algebraic and Geometric Topology, Tome 13 (2013) no. 5, pp. 3009-3029

Résumé

In this paper, we prove that there exists a new family of nontrivial homotopy elements in the stable homotopy groups of spheres with dimension q(pn + sp + 2) − 4. These nontrivial homotopy elements are represented by β̃sh0hn in the E2s+2,t–term of the Adams spectral sequence, where p ≥ 5, n > 4, p + 1 < s < 2p − 1, t = q(pn + sp + 2) + s − 2, q = 2(p − 1).

Détail

DOI : 10.2140/agt.2013.13.3009

Classification : 55Q45, 55T15, 55S10
Keywords: stable homotopy groups of spheres, Adams spectral sequence, May spectral sequence

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