منابع مشابه
A 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...
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We prove that for n ≥ 1 and q > 0 the (oriented) cobordism group of fold maps of (oriented) (n + q)-dimensional manifolds into R contains the direct sum of ⌊(q + 1)/2⌋ copies of the (n − 1)th stable homotopy group of spheres as a direct summand. We also prove that for k ≥ 1 and q = 2k − 1 the cobordism group of fold maps of unoriented (n+ q)-dimensional manifolds into R also contains the nth st...
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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 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 ...
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ژورنال
عنوان ژورنال: EMS magazine
سال: 2023
ISSN: ['2747-7894', '2747-7908']
DOI: https://doi.org/10.4171/mag/142