Modular representations and the homotopy of low rank p-local CW-complexes
نویسندگان
چکیده
منابع مشابه
MODULAR REPRESENTATIONS AND THE HOMOTOPY OF LOW RANK p-LOCAL CW -COMPLEXES
We construct an infinite set of retractions from certain loop spaces of suspended low rank CW -complexes X localized at an odd prime p. These retracts are themselves loop spaces of arbitrary suspensions of X. This is accomplished with the help of modular representations and their applications to topology.
متن کامل$G$-Weights and $p$-Local Rank
Let $k$ be field of characteristic $p$, andlet $G$ be any finite group with splitting field $k$. Assume that $B$ is a $p$-block of $G$.In this paper, we introduce the notion of radical $B$-chain $C_{B}$, and we show that the $p$-local rank of $B$ is equals the length of $C_{B}$. Moreover, we prove that the vertex of a simple $kG$-module $S$ is radical if and only if it has the same vertex of th...
متن کاملOn the Second Homotopy Module of Two-dimensional Cw Complexes
Let A' be a connected 2-dimensional CW complex. This note reproves from a very simple point of view two classical theorems of H. Hopf relating the homology of the fundamental group it = irx(X) of X and the Hurewicz map on ir2(X). This point of view also allows the dual theorems to be proved. If w is a finite group, a new interpretation is given for tf,(7r; Z) (/' = 2, 3) in terms of v2(X).
متن کاملcompactifications and representations of transformation semigroups
this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...
15 صفحه اولLocalizations, Fibrations, and Conic Structures 0.2. Lemma. for Any Cw{complexes A; X the Equivalence P a X ' Implies That Cw a X ' ?! X Is a Homotopy Equivalence
The aim of the present paper is to investigate some general properties of homotopy localization (and co{localization) with respect to a map f : A ! B, often with B '. The results give some understanding of the behavior of bre and coobre sequences under localizations. In particular we see how to commute localizations with the loop space functor. We give several applications in this paper and oth...
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: Mathematische Zeitschrift
سال: 2012
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-012-1027-7