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 module¶
-
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.
