Lagrangian matroids and cohomology (Q1575085)

The authors prove that \(\Delta\)-matroids associated with maps on compact closed surfaces are representable, with the space of representation provided by cohomology of the surface with punctured points. In particular, the main theorem states: Let \(X\) be a map with \(n\) edges on an orientable compact closed surface \(S\). Then all bases of \(X\) have cardinality \(n\) and the set of all bases is an orthogonally representable over \(\mathbb{Q}\), orthogonal Lagrangian matroid.