Maximal Sections of Sheaves of Data over an Abstract Simplicial Complex

Abstract

We employ techniques from topological data analysis to model sensor networks. Our approach to sensor integration uses the topological method of sheaves over cell complexes. The internal consistency of data from individual sensors is determined by a set of consistency functions assigned to elements of the complex. Using these functions we determine, for any collection of data, the unique set of maximal sections of consistent data received from the sensors. We offer a proof for the existence and uniqueness of these sections and illustrate the ideas with examples.