Arithmetic GFERF conjecture for quadratic-form hyperbolic manifolds
Arithmetic GFERF conjecture for quadratic-form hyperbolic manifolds
A hyperbolic manifold is arithmetic when its fundamental group is an arithmetic lattice. A subgroup is geometrically finite if its convex core has finite volume, and a lattice is GFERF when every geometrically finite subgroup is separable. Arithmetic GFERF conjecture. There exist compact arithmetic hyperbolic -manifolds defined by a quadratic form that are GFERF. The source states that the preceding conjecture on arbitrarily short geodesics would follow from this one by the same argument as the paper's main theorem; whether this conjecture has since been resolved is not specified in the supplied material.
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Primary source
Ian Agol, “Systoles of hyperbolic 4-manifolds”, arXiv:math/0612290 (2006).
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