An arithmetic square for virtually nilpotent spaces

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...

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 ...

Arithmetic Progressions with Square Entries

We study properties of arithmetic progressions consisting of three squares; in particular, how one arithmetic progression generates infinitely many others, by means of explicit formulas as well as a matrix method. This suggests an equivalence relation could be defined on the arithmetic progressions, which lead to interesting problems for further study. The purpose of this paper is to investigat...

Homogeneous Twistor Spaces And Nilpotent Orbits