Jacobian of a Metric Graph
The Jacobian is \(\mathrm{Jac}(\Gamma)=\Lambda_\mathbb{R}/\Lambda\), where \(\Lambda=H_1(\Gamma,\mathbb{Z})\) is the lattice of integer flows. The polarization is the cycle intersection pairing \([\cdot,\cdot]\).
Cycle flows (pick two)basis: zโ‚, zโ‚‚
Cycle lattice \(\Lambda = H_1(\Gamma,\mathbb{Z})\) hover a point ยท scroll to zoom ยท drag to pan
Intersection pairing & angle [ยท,ยท] = polarization