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Configuration Spaces of Repulsive Particles on a Metric Graph.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Configuration Spaces of Repulsive Particles on a Metric Graph./
Author:	Kim, Jimin.
Description:	1 online resource (102 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-05, Section: B.
Contained By:	Dissertations Abstracts International84-05B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798352630730

Configuration Spaces of Repulsive Particles on a Metric Graph.
Kim, Jimin.

Configuration Spaces of Repulsive Particles on a Metric Graph. - 1 online resource (102 pages)

Source: Dissertations Abstracts International, Volume: 84-05, Section: B.

Thesis (Ph.D.)--The Ohio State University, 2022.

Includes bibliographical references

We study the configuration space of points on a metric graph under the proximity condition where no two points can be closer than a constant number. We focus on how the topology of the configuration space changes. There are two main research frameworks: discrete Morse theory and the homological phase transition.We particularly consider the configuration space of points on a rooted tree. We find a discrete model that captures the homotopy type of the configuration. Applying discrete Morse theory gives us an upper bound to the dimension of the vanishing homology.We also look at a very specific example when a given tree is a star graph with three edges. We compute the Betti numbers of the configuration space of repulsive points on it. Beyond a unimodal trend of the Betti numbers, we also observe the homological phase transition in each dimension.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798352630730Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Configuration spaceIndex Terms--Genre/Form:

554714
Electronic books.

Configuration Spaces of Repulsive Particles on a Metric Graph.
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520 $a We study the configuration space of points on a metric graph under the proximity condition where no two points can be closer than a constant number. We focus on how the topology of the configuration space changes. There are two main research frameworks: discrete Morse theory and the homological phase transition.We particularly consider the configuration space of points on a rooted tree. We find a discrete model that captures the homotopy type of the configuration. Applying discrete Morse theory gives us an upper bound to the dimension of the vanishing homology.We also look at a very specific example when a given tree is a star graph with three edges. We compute the Betti numbers of the configuration space of repulsive points on it. Beyond a unimodal trend of the Betti numbers, we also observe the homological phase transition in each dimension.
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653 $a Morse theory
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653 $a Combinatorics
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