Dilatation phenomena in the homotopy groups of spheres
نویسندگان
چکیده
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...
متن کاملThe Dilatation Invariant in the Homotopy of Spheres
where f : Sm → Sn ranges all smooth representatives f of α. It has been conjectured by Olivier [5] that δ(α) is always an integer, which is still an open problem. The filtration invariant of α ∈ πm(S), filt(α), is the integer originally defined by James [2] in connection with his study of the reduced product construction. The definition is as follows [6]. For p,q ∈ Sn, n ≥ 2, let Ω∗ = Ω∗(Sn;p,q...
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 کاملOn the homotopy groups of spheres in homotopy type theory
The goal of this thesis is to prove that π4(S) ' Z/2Z in homotopy type theory. In particular it is a constructive and purely homotopy-theoretic proof. We first recall the basic concepts of homotopy type theory, and we prove some well-known results about the homotopy groups of spheres: the computation of the homotopy groups of the circle, the triviality of those of the form πk(S) with k < n, and...
متن کاملGroups of Homotopy Spheres: I
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...
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: Advances in Mathematics
سال: 1975
ISSN: 0001-8708
DOI: 10.1016/0001-8708(75)90135-8