AbstractsMathematics

On the topology of the spaces of coverings

by Han Wang




Institution: University of Illinois – Urbana-Champaign
Department: 0439
Degree: PhD
Year: 2015
Keywords: Covering
Record ID: 2057870
Full text PDF: http://hdl.handle.net/2142/72793


Abstract

The spaces of coverings (SoC) arise from various configuration spaces of the covering problems. We study the topology of these spaces for different domains and covering agents. In particular, we study the SoCs for grid domains and metric trees covered by balls. Characterizations of their topology are given for analysis of the topological complexities (the Betti numbers in all dimensions). We also study the spaces of fort coverings, a topological approximation of the SoCs capturing some essential features of the SoCs. The applications of the SoCs abound, in the end we present the feedback control on the SoC for metric tree coverage as a case study.