On the topology of the spaces of coverings

Covering;Topology;Configuration space;Feedback Control

Wang, Han

关键词: Covering;    Topology;    Configuration space;    Feedback Control;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/72793/Han_Wang.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.