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 ≤i ≤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.