Homological Domination in Large Random Simplicial Complexes
A. Costa and M. Farber
https://doi.org/10.19124/ima.2015.001.01
Abstract
Manifolds and simplicial complexes traditionally appear in robotics as configuration spaces of mechanical systems. The classical approach becomes inadequate if we are dealing with a large system, i.e. with a system depending on a large number of metric parameters, since these parameters cannot be measured without errors and small errors make significant impact on the structure of the obtained space. A more realistic approach for modelling large systems is based on the assumption that their configuration spaces are random with properties described using the language of probability theory…