Automatic Groups of 3-Manifolds

This database contains automatic groups for 5,389 of the 10,986 small-volume closed hyperbolic manifolds in the Hodgson–Weeks census.

AutomaticGroup(i): RngIntElt -> GrpAtc

AutomaticGroup(name): MonStgElt -> GrpAtc

AutomaticGroup(r): Rec -> GrpAtc

Returns the automatic group associated with the specified hyperbolic manifold, if present in the database. The manifold may be specified as an index \(i\) (\(1 \le i \le 5800\)), a name from the Hodgson–Weeks census, or a record from the manifold database (as described in Section Fundamental Groups of 3-Manifolds).

AutomaticGroupIndices() -> [RngIntElt]

Returns a sequence of the valid indices for use with AutomaticGroup.

AutomaticGroupNames() -> [MonStgElt]

Returns a sequence of the valid names for use with AutomaticGroup.