منابع مشابه
Homotopy Nilpotent Groups
We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that t...
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not null-homotopic such that [Z,X] [Z, f ] → [Z, Y ] is constant. For any X ′ ⊂ X with fewer than κ cells there exists X ′ → Z → X ′ = 1X′ , from which we may conclude that [X ′, X] [X ′, f ] → [X ′, Y ] is constant and in particular that f |X ′ is null-homotopic. Let H be the homotopy category obtained from T . Its objects are the objects of T , its maps are homotopy-classes of maps. The theor...
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Nilpotency for discrete groups can be defined in terms of central extensions. In this paper, the analogous definition for spaces is stated in terms of principal fibrations having infinite loop spaces as fibers, yielding a new invariant we compare with classical cocategory, but also with the more recent notion of homotopy nilpotency introduced by Biedermann and Dwyer. This allows us to character...
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Let P be an arbitrary set of primes. The P -nilpotent completion of a group G is defined by the group homomorphism η : G → G P̂ where G P̂ = invlim(G/ΓiG)P . Here Γ2G is the commutator subgroup [G,G] and ΓiG the subgroup [G,Γi−1G] when i > 2. In this paper, we prove that P -nilpotent completion of an infinitely generated free group F does not induce an isomorphism on the first homology group with...
متن کاملSelt homotopy equivalences of virtually nilpotent spaces *
The aim of this paper is to prove Theorem 1.1 below, a generalization to virtually nilpotent spaces of a result of Wilkerson [13] and Sullivan [12]. We recall that a CW complex Y is virtually nilpotent if (i) Y is connected, (ii) 7r~ Y is virtually nilpotent (i.e. has a nilpotent subgroup of finite index) and (iii) for every integer n > 1, zr~Y has a subgroup of finite index which acts nilpoten...
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ژورنال
عنوان ژورنال: Topology
سال: 1993
ISSN: 0040-9383
DOI: 10.1016/0040-9383(93)90017-p