A Hint at Differential Topology on Graphs
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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