%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 }