Curver Package API¶

Curver is a program for computations in the curve complex.

curver.kernel¶

The curver kernel.

Classes

 Arc A MultiArc with a single component. MultiArc An IntegralLamination in which every component is an Arc. Crush This represents the effect of crushing along a curve. Lift This represents the inverse of crushing along a curve. Curve A MultiCurve with a single component. MultiCurve An IntegralLamination in which every component is a Curve. CurveGraph This represents the curve complex of a surface. Encoding This represents a map between two Triangulations. Mapping An Encoding where every move is a FlipGraphMove. MappingClass A Mapping from a Triangulation to itself. HomologyClass This represents a homology class of a triangulation (relative to its vertices). Lamination This represents a lamination on a triangulation. MappingClassGroup This represents a triangulation along with a collection of named mapping classes on it. EdgeFlip Represents the change to a curve caused by flipping an edge. FlipGraphMove A Move between two triangulations in the same flip graph. Isometry This represents an isometry from one Triangulation to another. Move A basic move from one triangulation to another. Permutation This represents a permutation on 0, 1, …, N-1. Edge This represents an oriented edge, labelled with an integer. Triangle This represents a triangle. Triangulation This represents a triangulation of a punctured surface. HalfTwist This represents the effect of half-twisting a short arc. Twist This represents the effect of twisting a short curve.

curver.load.S_0_n(n)[source]
curver.load.S_1_n(n)[source]
curver.load.S_2_n(n)[source]
curver.load.S_3_n(n)[source]
curver.load.S_g_n(g, n)[source]
curver.load.load(*args)[source]

Return the requested example MappingClassGroup.

The mapping class group can either be specified by:

• a pair (g, n) in which case the Lickorish generating set is returned (see Figures 4.5 and 4.10 of [FarbMarg12]), or
• a string ‘S_g_n’ in which case the corresponding flipper / Twister generating set is returned.
curver.load.load_old(surface)[source]