smallCover -- create a small cover

Usage:

smallCover(K,lambda)
Inputs:
- K, an abstract simplicial complex,
- lambda, a matrix,
Outputs:
- a small cover,

Description

Create a small cover over K with characteristic matrix lambda. If lambda is not characteristic for K, then an error is returned. The entries of lambda are automatically converted to ZZ/2 entries, if they not already so.

The following example illustrates creating the 2-torus as a small cover over the unit square.

i1 : needsPackage "SimplicialComplexes"

o1 = SimplicialComplexes

o1 : Package

i2 : R = QQ[a..d]

o2 = R

o2 : PolynomialRing

i3 : K = simplicialComplex {a*b, b*c, c*d, d*a}

o3 = simplicialComplex | cd ad bc ab |

o3 : SimplicialComplex

i4 : lambda = matrix{{1, 0, 1, 0}, {0, 1, 0, 1}}

o4 = | 1 0 1 0 |
     | 0 1 0 1 |

              2       4
o4 : Matrix ZZ  <-- ZZ

i5 : X = smallCover(K, lambda)

o5 = SmallCover{QTMCharacteristicMatrix => | 1 0 1 0 |                   }
                                           | 0 1 0 1 |
                QTMDimension => 2
                QTMSimplicialComplex => simplicialComplex | cd ad bc ab |

o5 : SmallCover

For the programmer

The object smallCover is a method function.

The source of this document is in ToricTopology.m2:510:0.