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Use for questions regarding duality of mathematical object, i.e. dual spaces, objects with two possible interpretations etc.

13 votes
2 answers
1k views

Is there any relationship between the topologies of the clique complex and the independence ...

Playing around with small examples made me optimistic that there would be some way to relate the homology of $X(G)$ with the cohomology of $I(G)$, perhaps via Alexander Duality. … , where both $X(G)$ and $I(G)$ both have dimension roughly $2 \log_2 n$ and all their nontrivial homology concentrated around dimension $\log_2 n$, which also does not seem to bode well for Alexander Duality
Matthew Kahle's user avatar
10 votes
3 answers
2k views

Dual cell structures on manifolds

Suppose that $M$ is a compact manifold without boundary (smooth if you like), and suppose further that $M$ is equipped with a regular CW-complex structure. Denote the face poset of this CW-complex by …
Matthew Kahle's user avatar