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Topology of Coin Configuration Spaces By Haley Ervin
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Topology identifies two shapes as being equivalent if they can be continuously deformed into one another without cutting or gluing parts together. In the following thesis we study the topology of... More > coin configuration spaces. A coin configuration space models ways to arrange coins on a table. More precisely, each point in the coin configuration space represents a specific arrangement of n closed disks in the plane such that the union of the disks is connected and the interiors of the disks are disjoint. For various numbers of coins and under various assumptions, we study the questions: What does the configuration space look like, and what is its homology? How does adding and taking away coins change the space? In several cases, we answer these questions by placing a cell structure on the space. We use each cell structure to compute each space’s homology and Betti numbers, which give us a better idea of its topology.< Less

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