Dancing in the Stars: Topology of Non-k-equal Configuration Spaces of Graphs
| dc.contributor.advisor | Sinha, Dev | |
| dc.contributor.author | Chettih, Safia | |
| dc.date.accessioned | 2016-11-21T17:00:59Z | |
| dc.date.available | 2016-11-21T17:00:59Z | |
| dc.date.issued | 2016-11-21 | |
| dc.description.abstract | We prove that the non-k-equal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit combinatorial formula for the ranks of homology and cohomology of configurations of two points on a tree. We give explicit presentations for homology and cohomology classes as well as pairings for ordered and unordered configurations of two and three points on a few simple trees, and show that the first homology group of ordered and unordered configurations of two points in any tree is generated by the first homology groups of configurations of two points in three particular graphs, K_{1,3}, K_{1,4}, and the trivalent tree with 6 vertices and 2 vertices of degree 3, via graph embeddings. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/20728 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | Creative Commons BY-NC 4.0-US | |
| dc.subject | Configuration space | en_US |
| dc.subject | Discrete Morse theory | en_US |
| dc.subject | Graph braid group | en_US |
| dc.subject | Non-k-equal configuration | en_US |
| dc.title | Dancing in the Stars: Topology of Non-k-equal Configuration Spaces of Graphs | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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