An n-pointed configuration space of a topological space X parametrizes n distinct points in X. Configuration spaces of higher dimensional manifolds have been studied widely, but less is known when X is a graph. We consider a family of graphs $G_n$ with compatible $S_n$-actions. Fixing the number of points k, the homology groups of the k-configuration spaces of these graphs exhibit representation stability for many families. Examples include the star graphs, complete graphs, and the Kneser graphs. Our goal is to explicitly compute these stable representations. We use a discretized model for the configuration spaces developed by Abrams that has a cellular decomposition in terms of the combinatorics of the graphs and we perform our computations in the software system SageMath. We will present some partial results in the cases k=2 and G is a star graph and a complete graph. This is joint work with Eric Ramos.

Note regarding location: The Pillsbury room is located on Floor 4M on the Psychology side of East Hall. To get to the room, you enter the Psychology side of East Hall from the Church Street entrance and before you get into the Psych atrium, there is an elevator to your left. Take the elevator to Floor 4M and the elevator opens into the room.

Note regarding location: The Pillsbury room is located on Floor 4M on the Psychology side of East Hall. To get to the room, you enter the Psychology side of East Hall from the Church Street entrance and before you get into the Psych atrium, there is an elevator to your left. Take the elevator to Floor 4M and the elevator opens into the room.

Building: | East Hall |
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Event Type: | Presentation |

Tags: | Mathematics, seminar |

Source: | Happening @ Michigan from Representation Stability Seminar - Department of Mathematics, Department of Mathematics |