Mathematics Colloquia and Seminars

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Knowledge of one area of math can often provide intuition and information about another. For nice manifolds, we have a graph with some added structure associated with it. Now we can redefine topological terminology general enough to apply to all graphs, including those that don't have a manifold associated with them. In particular, we'll define the Betti numbers and use them to solve some classical combinatorial problems like counting the number of n-k dimensional faces of a simple convex polytope.