A Hint at Differential Topology on Graphs

Tara Holm


October 31,
refreshments at 3:45pm


We study a natural family of graphs associated to symplectic manifolds with torus actions. These graphs encode information about the manifold, in particular they are useful for computations in equivariant cohomology. For this reason, it is important to understand the combinatorics and combinatorial significance of the structures inherited from the geometric setting. Accordingly, we can start with a graph $\Gamma$, and define combinatorial analogues of geometric objects, including Morse functions and Betti numbers. We will examine several examples, and then state theorems about these objects, some motivated by differential geometry and topology, and some purely combinatorial. I will not assume any background in symplectic geometry.

Speaker's Contact Info: tsh(at-sign)math.mit.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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