The Gauss-Bonnet-Chern theorem: a probabilistic perspective
Differential Geometry
2016-01-19 v3 Analysis of PDEs
Probability
Abstract
We prove that the Euler form of a metric connection on real oriented vector bundle over a compact oriented manifold can be identified, as a current, with the expectation of the random current defined by the zero-locus of a certain random section of the bundle. We also explain how to reconstruct probabilistically the metric and the connection on from the statistics of random sections of .
Keywords
Cite
@article{arxiv.1404.5206,
title = {The Gauss-Bonnet-Chern theorem: a probabilistic perspective},
author = {Liviu I. Nicolaescu and Nikhil Savale},
journal= {arXiv preprint arXiv:1404.5206},
year = {2016}
}
Comments
35 pages, references added, fixed typos, to appear Trans. Amer. Math. Soc