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Title:On the topology of the spaces of coverings
Author(s):Wang, Han
Director of Research:Baryshnikov, Yuliy
Doctoral Committee Chair(s):Schenck, Hal
Doctoral Committee Member(s):Baryshnikov, Yuliy; Hirani, Anil; Zharnitsky, Vadim
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Covering
Topology
Configuration space
Feedback Control
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.
Issue Date:2015-01-21
URI:http://hdl.handle.net/2142/72793
Rights Information:Copyright 2014 Han Wang
Date Available in IDEALS:2015-01-21
Date Deposited:2014-12


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