ProV Logo
0
Proalgebraic crossed modules of quasirat...
Mikhovich, Andrey...

Free

Proalgebraic crossed modules of quasirational presentations by Mikhovich, Andrey ( Author )
Lemonjar Open Access
N.A
11-07-2015
We introduce the concept of quasirational relation modules for discrete and pro-p presentations of discrete and pro-p groups and show that aspherical presentations and their subpresentations are quasirational. In the pro-p-case quasirationality of pro-p-groups with a single defining relation holds. For every quasirational (pro-p)relation module we construct the so called p-adic rationalization, which is a pro-fd-module R¯¯¯¯⊗ˆQp=lim←−R/[R,RMn]⊗Qp. We provide the isomorphisms R∧w¯¯¯¯¯¯¯(Qp)=R¯¯¯¯⊗ˆQp and Ru¯¯¯¯¯¯(Qp)=O(Gu)∗, where R∧w and R∧u stands for continuous prounipotent completions and corresponding prounipotent presentations correspondingly. We show how R∧w¯¯¯¯¯¯¯ embeds into a sequence of abelian prounipotent groups. This sequence arises naturally from a certain prounipotent crossed module, the latter bring concrete examples of proalgebraic homotopy types. The old-standing open problem of Serre, slightly corrected by Gildenhuys, in its modern form states that pro-p-groups with a single defining relation are aspherical. Our results give a positive feedback to the question of Serre.
-
Article
pdf
36.88 KB
English
-
MYR 0.00
-
https://arxiv.org/abs/1507.03155
Share this eBook