Math RefereeArithmeticity, superrigidity, and totally geodesic submanifolds
Uri Bader, David Fisher, Nicholas Miller and Matthew Stover
The proposed argument
The proposed argument translates infinitely many maximal totally geodesic subspaces into homogeneous measures approaching Haar measure, lifts them to a projective bundle, and uses compatibility and algebraic representations to extend lattice representations. A trace-field/local-place criterion then yields arithmeticity; separate deductions address knot complements, geometric finiteness and Dehn fillings.
The reading materials use the 23-page arXiv v5. The Annals article occupies 25 journal pages; selected passages were separately compared with the frozen journal manuscript. The received-date external-input cutoff is 20 June 2019.
Reading order
- 01
Geometry to homogeneous measures
Read the geometric and homogeneous formulations, then the closed-orbit and measure-convergence arguments.
- 02
Lift the measures
Follow how algebraic subgroups provide invariant lines and measures on a projective bundle. Keep the three-dimensional representation case separate.
- 03
Compatibility and superrigidity
Identify the allowed target groups, then follow initial algebraic representations, normalizer equivariance and the continuous extension.
- 04
Arithmeticity and applications
Return to the adjoint trace field and its places, then read the knot, geometric-finiteness and Dehn-filling deductions separately.
Follow the dependencies
Open the full map ↗Select a claim to see its prerequisites and consumers. Edge labels distinguish proof inputs, source references, background and exclusions.
Your independent assessment
Trace the geometric-to-measure reduction, projective-bundle construction, compatibility condition and superrigidity theorem. Check the adjoint trace-field deduction and each application with its own hypotheses.