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Dissertation/Thesis Abstract

Dancing in the stars: Topology of non-k-equal configuration spaces of graphs
by Chettih, Safia, Ph.D., University of Oregon, 2016, 82; 10193648
Abstract (Summary)

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, K1,3, K1,4, and the trivalent tree with 6 vertices and 2 vertices of degree 3, via graph embeddings.

Indexing (document details)
Advisor: Sinha, Dev
Commitee: Botvinnik, Boris, Livelybrooks, Dean, Sadofsky, Hal, Vologodski, Vadim
School: University of Oregon
Department: Department of Mathematics
School Location: United States -- Oregon
Source: DAI-B 78/04(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Configuration space, Discrete Morse theory, Graph braid group, Non-k-equal configuration
Publication Number: 10193648
ISBN: 978-1-369-35974-9
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