Title page for ETD etd-10072005-173425


Type of Document Dissertation
Author Ison, Molly E.
URN etd-10072005-173425
Title Two Aspects of Topology in Graph Configuration Spaces
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Haskell, Peter E. Committee Chair
Brown, Ezra A. Committee Member
Farkas, Daniel R. Committee Member
Keywords
  • fundamental group
  • pseudomanifold with boundary
  • manifold
  • braid group
  • graph
  • configuration space
Date of Defense 2005-10-07
Availability unrestricted
Abstract
A graph configuration space is generated by the movement of a finite number of robots on a graph. These configuration spaces of points in a graph are topologically interesting objects. By using local, combinatorial properties, we define a new classification of graphs whose configuration spaces are pseudomanifolds with boundary. In algebraic topology, graph configuration spaces are closely related to classical braid groups, which can be described as fundamental groups of configuration spaces of points in the plane. We examine this relationship by finding a presentation for the fundamental group of one graph configuration space.
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