Orthogonality and Minimality in the Homology of Locally Finite Graphs

Given a finite set E, a subset D ✓ E (viewed as a function E ! F2) is orthogonal to a given subspace F of the F2-vector space of functions E ! F2 as soon as D is orthogonal to every ✓-minimal element of F . This fails in general when E is infinite. However, we prove the above statement for the six subspaces F of the edge space of any 3-connected locally finite graph that are relevant to its homology: the topological, algebraic, and finite cycle and cut spaces. This solves a problem of [5].