A tensor product approach to non-local differential complexes
Functional Analysis
2022-11-02 v1 Algebraic Topology
Metric Geometry
Abstract
We study differential complexes of Kolmogorov-Alexander-Spanier type on metric measure spaces associated with unbounded non-local operators, such as operators of fractional Laplacian type. We define Hilbert complexes, observe invariance properties and obtain self-adjoint non-local analogues of Hodge Laplacians. For -regular measures and operators of fractional Laplacian type we provide results on removable sets in terms of Hausdorff measures. We prove a Mayer-Vietoris principle and a Poincar\'e lemma and verify that in the compact Riemannian manifold case the deRham cohomology can be recovered.
Cite
@article{arxiv.2211.00343,
title = {A tensor product approach to non-local differential complexes},
author = {Michael Hinz and Jörn Kommer},
journal= {arXiv preprint arXiv:2211.00343},
year = {2022}
}