Proximal Planar Shapes. Correspondence between Shapes and Nerve Complexes
Metric Geometry
2018-05-25 v4
Abstract
This article considers proximal planar shapes in terms of the proximity of shape nerves and shape nerve complexes. A shape nerve is collection of 2-simplexes with nonempty intersection on a triangulated shape space. A planar shape is a shape nerve complex, which is a collection of shape nerves that have nonempty intersection. A main result in this paper is the homotopy equivalence of a planar shape nerve complex and the union of its nerve sub-complexes.
Cite
@article{arxiv.1708.04147,
title = {Proximal Planar Shapes. Correspondence between Shapes and Nerve Complexes},
author = {James F. Peters},
journal= {arXiv preprint arXiv:1708.04147},
year = {2018}
}
Comments
13 pages, 5 figures. arXiv admin note: text overlap with arXiv:1704.05909