Date started: 2018
Leads: Joseph Quinn, Alberto Verjovsky
We gave a way of computing fundamental domains for Sol 3-manifolds that accurately reflects their geometric structure, as a stack of tori where the bottom glues to the top by an Anosov diffeomorphism (we choose to scale these logarithmically to better see the shape). At the ICERM event, I’m working on: sharing this result to improve visualization technology for these manifolds, extending the result to visualize slices of Hilbert modular surfaces (not just the cusps).
Each Sol 3-manifold construction starts with a square free . Here are four examples.
Cusp shapes of Hilbert-Blumenthal surfaces, Joseph Quinn and Alberto Verjovsky, 2019, Geometriae Dedicata, DOI:10.1007/s10711-019-00474-w (arXiv:1711.02418)