Measuring Shape with Topology
Algebraic Topology
2010-12-20 v2 Materials Science
Computational Geometry
Mathematical Physics
math.MP
Abstract
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We demonstrate the utility and computability of this measure by applying it to branched polymers, Brownian trees, and self-avoiding random walks.
Cite
@article{arxiv.1011.2258,
title = {Measuring Shape with Topology},
author = {Robert MacPherson and Benjamin Schweinhart},
journal= {arXiv preprint arXiv:1011.2258},
year = {2010}
}
Comments
19 pages, 8 figures