PreprintCC BY 4.0arXiv
Spectral complexes and currents on the Engel group
Abstract
We study the spectral complexes arising from the de Rham complex on the Engel group G viewed as a truncated multicomplex. We describe the two resulting complexes, analyse their compactly supported counterparts, and define the corresponding spectral currents by duality. We prove that the smooth spectral complexes embed naturally into the current complexes. Finally, we show that the Pansu pullback of a Wloc1,q map φ: G→ G with q>7 induces a morphism into the corresponding complexes of spectral currents.
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BibTeX
@misc{biundo2026spectral,
title = {{Spectral complexes and currents on the Engel group}},
author = {Filippa Lo Biundo and Francesca Tripaldi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11625},
eprint = {2609.11625},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11625},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral complexes and currents on the Engel group
AU - Filippa Lo Biundo
AU - Francesca Tripaldi
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11625
UR - https://arxiv.org/abs/2609.11625
AB - We study the spectral complexes arising from the de Rham complex on the Engel group G viewed as a truncated multicomplex. We describe the two resulting complexes, analyse their compactly supported counterparts, and define the corresponding spectral currents by duality. We prove that the smooth spectral complexes embed naturally into the current complexes. Finally, we show that the Pansu pullback of a W_loc^1,q map φ: G→ G with q>7 induces a morphism into the corresponding complexes of spectral currents.
ER -