Macaulay2 » Documentation
Packages » SimplicialComplexes :: elementaryCollapse(SimplicialComplex,RingElement)
next | previous | forward | backward | up | index | toc

elementaryCollapse(SimplicialComplex,RingElement) -- construct the elementary collapse of a free face in a simplicial complex

Description

A free face of a simplicial complex $\Delta$ is a face that is a proper maximal subface of exactly one facet. The elementary collapse is the simplicial complex obtained by removing the free face, and the facet containing it, from $\Delta$. A simplicial complex that can be collapsed to a single vertex is called collapsible. Every collapsible simplicial complex is contractible, but the converse is not true.

i1 : R = ZZ/103[x_0..x_3];
 
i2 : Δ = simplicialComplex{R_0*R_1*R_2,R_0*R_2*R_3,R_0*R_1*R_3}

o2 = simplicialComplex | x_0x_2x_3 x_0x_1x_3 x_0x_1x_2 |

o2 : SimplicialComplex
 
i3 : C1 = elementaryCollapse(Δ,R_1*R_2)

o3 = simplicialComplex | x_0x_2x_3 x_0x_1x_3 |

o3 : SimplicialComplex
 
i4 : C2 = elementaryCollapse(C1,R_2*R_3)

o4 = simplicialComplex | x_0x_2 x_0x_1x_3 |

o4 : SimplicialComplex
 
i5 : C3 = elementaryCollapse(C2,R_1*R_3)

o5 = simplicialComplex | x_0x_3 x_0x_2 x_0x_1 |

o5 : SimplicialComplex
 
i6 : C4 = elementaryCollapse(C3,R_1)

o6 = simplicialComplex | x_0x_3 x_0x_2 |

o6 : SimplicialComplex
 
i7 : C5 = elementaryCollapse(C4,R_2)

o7 = simplicialComplex | x_0x_3 |

o7 : SimplicialComplex
 
i8 : C6 = elementaryCollapse(C5,R_3)

o8 = simplicialComplex | x_0 |

o8 : SimplicialComplex

See also

Ways to use this method:

The source of this document is in SimplicialComplexes/Documentation.m2:4552:0.