Does a space enjoying good finiteness properties admit an algebraic model with commensurable finiteness properties? In this note, we provide a rational homotopy obstruction for this to happen. As an application, we show that the maximal metabelian quotient of a very large, finitely generated group is not finitely presented. Using the theory of 1‐minimal models, we also show that a finitely generated group
π admits a connected 1‐model with finite‐dimensional degree 1 piece if and only if the Malcev Lie algebra m(π) is the lower central series completion of a finitely presented Lie algebra.
%0 Journal Article
%1 PapadimaSuciuNov2017
%A Papadima, Stefan
%A Suciu, Alexander I.
%D 2019
%J Journal of the London Mathematical Society
%K myown
%N 1
%P 173-193
%R 10.1112/jlms.12169
%T Infinitesimal finiteness obstructions
%U https://arxiv.org/abs/1711.07085
%V 99
%X Does a space enjoying good finiteness properties admit an algebraic model with commensurable finiteness properties? In this note, we provide a rational homotopy obstruction for this to happen. As an application, we show that the maximal metabelian quotient of a very large, finitely generated group is not finitely presented. Using the theory of 1‐minimal models, we also show that a finitely generated group
π admits a connected 1‐model with finite‐dimensional degree 1 piece if and only if the Malcev Lie algebra m(π) is the lower central series completion of a finitely presented Lie algebra.
@article{PapadimaSuciuNov2017,
abstract = {Does a space enjoying good finiteness properties admit an algebraic model with commensurable finiteness properties? In this note, we provide a rational homotopy obstruction for this to happen. As an application, we show that the maximal metabelian quotient of a very large, finitely generated group is not finitely presented. Using the theory of 1‐minimal models, we also show that a finitely generated group
π admits a connected 1‐model with finite‐dimensional degree 1 piece if and only if the Malcev Lie algebra m(π) is the lower central series completion of a finitely presented Lie algebra.},
added-at = {2017-11-21T03:44:00.000+0100},
author = {Papadima, Stefan and Suciu, Alexander I.},
biburl = {https://www.bibsonomy.org/bibtex/2d5dc141a19dee3d2d81181983f25774f/asuciu},
doi = {10.1112/jlms.12169},
interhash = {ee9adba77b2588fdabcee6f6cc676d3b},
intrahash = {d5dc141a19dee3d2d81181983f25774f},
journal = {Journal of the London Mathematical Society},
keywords = {myown},
month = feb,
number = 1,
pages = {173-193},
timestamp = {2019-02-02T00:04:14.000+0100},
title = {Infinitesimal finiteness obstructions},
url = {https://arxiv.org/abs/1711.07085},
volume = 99,
year = 2019
}