Bowditch–Maclachlan–Reid finiteness conjecture
For every integer , there are only finitely many cyclic commensurability classes of closed, fibered arithmetic hyperbolic -manifolds having a fiber of genus .
References
Primary source
Additional references
- Finiteness of closed arithmetic hyperbolic surface bundles — arXiv — Tam Cheetham-West, Homin Lee, Nicholas Miller
Progress summary
A new unrefereed preprint claims to prove the conjecture, but the result has not yet been independently verified.
The Bowditch–Maclachlan–Reid conjecture predicts a finiteness phenomenon for arithmetic hyperbolic surface bundles. No proposer or original date is identified in the retrieved material.
September 2026 preprint
Tam Cheetham-West, Homin Lee, and Nicholas Miller claim a proof of the conjectured finiteness, alongside a broader finiteness theorem and effective asymptotic bounds. The work is presented as a new unrefereed preprint, so the claimed resolution remains unconfirmed.
Current status (as of September 2026): A September 2026 preprint claims to settle the conjecture and obtain stronger quantitative results, but independent verification and refereeing are outstanding.
Solutions 0
No solutions have been posted yet.