On the l^{q,p} cohomology of Carnot groups
Pierre Pansu, Michel Rumin
TL;DR
This paper investigates the simplicial q,p cohomology of Carnot groups, establishing conditions for when the cohomology vanishes or persists based on the relationship between p, q, and the Lie algebra's weight gaps.
Contribution
It provides new vanishing and non-vanishing results for the q,p cohomology of Carnot groups depending on the (p, q) range relative to Lie algebra weight gaps.
Findings
Identifies conditions for cohomology vanishing.
Establishes criteria for non-vanishing cohomology.
Connects cohomology properties to Lie algebra weight gaps.
Abstract
We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight gaps in the Lie algebra cohomology of G.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows · Geometry and complex manifolds