Sobolev mappings and the spectral sequence for Rumin's filtration on the de Rham complex
Differential Geometry
2022-05-10 v1
Abstract
We consider Rumin's filtration on the de Rham complex of a Carnot group. Although Pansu pullback by a Sobolev map is filtration preserving, it need not be a chain mapping. Nonetheless, we show that Pansu pullback induces a mapping of the associated spectral sequences. This gives an alternate interpretation of the Pullback Theorem from our previous paper.
Keywords
Cite
@article{arxiv.2205.04302,
title = {Sobolev mappings and the spectral sequence for Rumin's filtration on the de Rham complex},
author = {Bruce Kleiner and Stefan Muller and Xiangdong Xie},
journal= {arXiv preprint arXiv:2205.04302},
year = {2022}
}