A New Approach to Euler Calculus for Continuous Integrands
Differential Geometry
2015-11-05 v2 Algebraic Geometry
Algebraic Topology
Combinatorics
Abstract
Euler calculus is based on integrating simple functions with respect to the Euler characteristic. This paper makes the case for extending Euler calculus to continuous integrands by integrating with respect to (Gaussian) curvature. This requires a metric but is nevertheless defined within any O-minimal theory. It satisfies a Fubini theorem and extends to a functor. Euler calculus is the "adiabatic limit" of this "curvature calculus". All this suggests new applications of differential geometry to data analysis.
Cite
@article{arxiv.1511.00257,
title = {A New Approach to Euler Calculus for Continuous Integrands},
author = {Carl McTague},
journal= {arXiv preprint arXiv:1511.00257},
year = {2015}
}
Comments
16 pages, 12 figures; 3d-figures now rasterized, an egregious spelling error corrected