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arXiv · 2205.04302

Sobolev mappings and the spectral sequence for Rumin's filtration on the de Rham complex

Bruce Kleiner·Stefan Muller·Xiangdong Xie
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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.

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Bruce Kleiner, Stefan Muller, Xiangdong Xie. 2022-05-09. Sobolev mappings and the spectral sequence for Rumin's filtration on the de Rham complex. https://arxiv.org/abs/2205.04302

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