Nilpotent spaces of sections

Nilpotent Spaces of Sections

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Cellular properties of nilpotent spaces

We show that cellular approximations of nilpotent Postnikov stages are always nilpotent Postnikov stages, in particular classifying spaces of nilpotent groups are turned into classifying spaces of nilpotent groups. We use a modified Bousfield–Kan homology completion tower zkX whose terms we prove are all X–cellular for any X . As straightforward consequences, we show that if X is K–acyclic and ...

Selt 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...

Extension of Maps to Nilpotent Spaces Iii

Linear Spaces of Toeplitz and Nilpotent Matrices

Let F be an arbitrary field and let J¢/', (F) denote the linear space of all matrices of order n over F. Let W be a subspace of J/t, (F). Let r be an integer with 1 ~< r ~ n. Flanders [21 considered the question of how large the dimension of W must be to guarantee that W contains a matrix whose rank is at least equal to r. There exist spaces W of dimension ( r 1 ) n containing no matrix of rank...