Topology#
Sage includes some tools for topology, and in particular cell complexes: (filtered) simplicial complexes, \(\Delta\)-complexes, cubical complexes, and simplicial sets. A class of generic cell complexes is also available, mainly for developers who want to use it as a base for other types of cell complexes.
- Finite simplicial complexes
- Morphisms of simplicial complexes
- Homsets between simplicial complexes
- Examples of simplicial complexes
BarnetteSphere()BrucknerGrunbaumSphere()ChessboardComplex()ComplexProjectivePlane()DunceHat()FareyMap()GenusSix()K3Surface()KleinBottle()MatchingComplex()MooreSpace()NotIConnectedGraphs()PoincareHomologyThreeSphere()ProjectivePlane()QuaternionicProjectivePlane()RandomComplex()RandomTwoSphere()RealProjectivePlane()RealProjectiveSpace()RudinBall()ShiftedComplex()Simplex()Sphere()SumComplex()SurfaceOfGenus()Torus()UniqueSimplicialComplexZieglerBall()facets_for_K3()facets_for_RP4()matching()
- Finite Delta-complexes
- Finite cubical complexes
- Simplicial sets
- Methods of constructing simplicial sets
ConeOfSimplicialSetConeOfSimplicialSet_finiteDisjointUnionOfSimplicialSetsDisjointUnionOfSimplicialSets_finiteFactorsProductOfSimplicialSetsProductOfSimplicialSets_finitePullbackOfSimplicialSetsPullbackOfSimplicialSets_finitePushoutOfSimplicialSetsPushoutOfSimplicialSets_finiteQuotientOfSimplicialSetQuotientOfSimplicialSet_finiteReducedConeOfSimplicialSetReducedConeOfSimplicialSet_finiteSmashProductOfSimplicialSets_finiteSubSimplicialSetSuspensionOfSimplicialSetSuspensionOfSimplicialSet_finiteWedgeOfSimplicialSetsWedgeOfSimplicialSets_finite
- Examples of simplicial sets.
- Catalog of simplicial sets
- Morphisms and homsets for simplicial sets
- Generic cell complexes
- Finite filtered complexes