Polynomial Cohomology and Polynomial Maps on Nilpotent Groups
Abstract
We introduce a refined version of group cohomology and relate it to the space of polynomials on the group in question. We show that the polynomial cohomology with trivial coefficients admits a description in terms of ordinary cohomology with polynomial coefficients, and that the degree one polynomial cohomology with trivial coefficients admits a description directly in terms of polynomials. Lastly, we give a complete description of the polynomials on a connected, simply connected nilpotent Lie group by showing that these are exactly the maps that pull back to classical polynomials via the exponential map.
Cite
@article{arxiv.1503.04068,
title = {Polynomial Cohomology and Polynomial Maps on Nilpotent Groups},
author = {David Kyed and Henrik Densing Petersen},
journal= {arXiv preprint arXiv:1503.04068},
year = {2020}
}
Comments
v3: minor changes; to appear in Glasgow Mathematical Journal. v2: significant changes compared to v1; the result on quasi-isometry classification of csc nilpotent Lie groups removed due to a flaw in the proof