A Conformal de Rham Complex
Vladimir Gol'dshtein, Marc Troyanov
TL;DR
This paper introduces a conformal de Rham complex for Riemannian manifolds, a new invariant under quasiconformal maps, enriching the tools for geometric analysis.
Contribution
It defines a conformal de Rham complex as a graded differential Banach algebra invariant under quasiconformal maps, providing a novel quasiconformal invariant.
Findings
The conformal de Rham complex is a graded differential Banach algebra.
It is invariant under quasiconformal maps.
The associated cohomology serves as a new quasiconformal invariant.
Abstract
We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the associated cohomology is a new quasiconformal invariant.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology