Topological complexity of graph configuration spaces

Topological complexity of graph configuration spaces

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Steve Scheirer, Lehigh University
Fine Hall 214

The topological complexity of a path-connected space X, denoted by TC(X), is an integer which can be thought of as the minimum number of "continuous rules" required to describe how to move between any two points of X. We will consider the case in which X is a space of configurations of n points on a graph.  This space can be viewed as the space of configurations of n robots which move along a system of one-dimensional tracks.  We will recall Farley and Sabalka's approach to studying these spaces using discrete Morse theory and discuss how this can be used to determine the topological complexity.