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

TL;DR

This paper explores how Pansu pullback interacts with Rumin's filtration on the de Rham complex in Carnot groups, revealing that it induces a spectral sequence mapping despite not being a chain map.

Contribution

It demonstrates that Pansu pullback induces a spectral sequence map on Rumin's filtration, providing an alternative perspective on the Pullback Theorem.

Findings

Pansu pullback preserves filtration but not chain structure

Induces a spectral sequence map for Rumin's filtration

Offers an alternative interpretation of the Pullback Theorem

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.