The homotopy groups of the integral cycle groups
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 کاملPresentations of the First Homotopy Groups of the Unitary Groups
We describe explicit presentations of all stable and the first nonstable homotopy groups of the unitary groups. In particular, for each n ≥ 2 we supply n homotopic maps that each represent the (n − 1)!-th power of a suitable generator of π2nSU(n) ≈ Zn!. The product of these n commuting maps is the constant map to the identity matrix. Introduction The homotopy groups of compact Lie groups have b...
متن کاملHomotopy Groups of Compact Abelian Groups
Preliminaries. Bn (resp. 5„_i) will denote the subset of Rn consisting of those x such that ||x|| g 1 (resp. ¡|x|| = 1). x0 will denote the point (1, 0, 0, •• -, 0) of R" and T will denote Si made into a topological group by using complex multiplication. All groups will be assumed to be Abelian. For a based topological space X and a topological group G, let C(X, G) denote the set of maps (i.e.,...
متن کاملThe Stable Homotopy of the Classical Groups.
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. 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 o...
متن کاملOn braid groups and homotopy groups
The purpose of this article is to give an exposition of certain connections between the braid groups [1, 3] and classical homotopy groups which arises in joint work of Jon Berrick, Yan-Loi Wong and the authors [8, 2, 32]. These connections emerge through several other natural contexts such as Lie algebras attached to the descending central series of pure braid groups arising as Vassiliev invari...
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: Topology
سال: 1962
ISSN: 0040-9383
DOI: 10.1016/0040-9383(62)90016-2