Detection of Some Elements in the Stable Homotopy Groups of Spheres |
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Authors: | Xiugui LIU |
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Affiliation: | School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China |
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Abstract: | Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π * S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres which is of order p and is represented by k 0 h n ∈ (ℤ p, ℤp ) in the Adams spectral sequence, where p ≥ 5 is an odd prime, n ≥ 3 and q = 2(p − 1). In the course of the proof, a new family of homotopy elements in which is represented by β * i′* i *(h n ) ∈ (H * V(1), ℤ p ) in the Adams sequence is detected. Project supported by the National Natural Science Foundation of China (Nos. 10501045, 10771105) and the Fund of the Personnel Division of Nankai University (No. J02017). |
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Keywords: | Stable homotopy groups of spheres Adams spectral sequence May spectral sequence Steenrod algebra |
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