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On the topology of the spaces of coverings
Wang, Han
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https://hdl.handle.net/2142/72793
Description
- Title
- On the topology of the spaces of coverings
- Author(s)
- Wang, Han
- Issue Date
- 2015-01-21
- Director of Research (if dissertation) or Advisor (if thesis)
- Baryshnikov, Yuliy
- Doctoral Committee Chair(s)
- Schenck, Hal
- Committee Member(s)
- Baryshnikov, Yuliy
- Hirani, Anil
- Zharnitsky, Vadim
- Department of Study
- Mathematics
- Discipline
- Mathematics
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Date of Ingest
- 2015-01-21T19:48:15Z
- Keyword(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.
- Graduation Semester
- 2014-12
- Permalink
- http://hdl.handle.net/2142/72793
- Copyright and License Information
- Copyright 2014 Han Wang
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Graduate Dissertations and Theses at Illinois PRIMARY
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