An application of complex bordism to the stable homotopy groups of spheres

An Application of Complex Bordism to the Stable Homotopy Groups of Spheres

X a finite complex. This has brought us into contact with many new and interesting questions concerning the readabi l i ty of certain cyclic S2*-modules as complex bordism modules of finite complexes. Needless to say it has also involved us in the stable homotopy groups of spheres, particularly with the occurrence of certain types of infinite families of elements in the ^-component (see the dis...

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...

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 ...

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...

Complex Cobordism and Stable Homotopy Groups of Spheres