A Nontrivial Product in the Stable Homotopy of Spheres
نویسندگان
چکیده
منابع مشابه
Detection 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 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 کاملA Nontrivial Product of Filtration s+ 5 in the Stable Homotopy of Spheres
In this paper, some groups Ext A (Zp, Zp) with specialized s and t are first computed by the May spectral sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q−5S which is represented (up to a nonzero scalar) by β̃s+2b0hn ∈ Ext q+(s+3)pq+(s+1)q+s A (Zp, Zp) in the ...
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied and Computational Mathematics
سال: 2017
ISSN: 2328-5605
DOI: 10.11648/j.acm.20170604.17