Homocyclic Jacobians of planar biconnected graphs
For every r ≥ 1, we construct a simple planar biconnected graph with 2r + 2 vertices, 4r + 1 edges, maximum degree at most four, and Jacobian (ℤ/8ℤ)^r. This disproves the bounded-multiplicity conjecture of Gaudet, Jensen, Ranganathan, Wawrykow and Weisman. We give explicit generators and compute the monodromy pairing:...