A priori bounds for geodesic diameter. Part I. Integral chains with coefficients in a complete normed commutative group
Abstract
As service to the community, we provide - for Euclidean space - a basic treatment of locally rectifiable chains and of the complex of locally integral chains. In this setting, we may beneficially develop the idea of a complete normed commutative group bundle over the Grassmann manifold whose fibre is the coefficient group of the chains. Our exposition also sheds new light on some algebraic aspects of the theory. Finally, we indicate an extension to a geometric approach to locally flat chains centring on locally rectifiable chains rather than completion procedures.
Keywords
Cite
@article{arxiv.2206.14046,
title = {A priori bounds for geodesic diameter. Part I. Integral chains with coefficients in a complete normed commutative group},
author = {Ulrich Menne and Christian Scharrer},
journal= {arXiv preprint arXiv:2206.14046},
year = {2024}
}
Comments
41 pages, five diagrams. This is the first paper of a series of three papers which shall supersede arXiv:1709.05504 by the same authors. v2: Amended acknowledgement with Max Planck Institute for Mathematics in the Sciences, updated list of references