On the topology of the spaces of coverings

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Wang, Han

Contributors dc:contributor

• Baryshnikov, Yuliy
• Schenck, Hal
• Hirani, Anil
• Zharnitsky, Vadim

• Covering
• Topology
• Configuration space
• Feedback Control

Statement dc:rights

• Copyright 2014 Han Wang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/72793

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72793