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ToricTopology :: ToricTopology

ToricTopology -- homological computations in toric topology

Description

ToricTopology is a package for computing with quasi-toric manifolds and small covers.

A quasi-toric manifold (or small cover) is entirely determined by a pair consisting of a simplicial complex K and a matrix chi which is characteristic for K.

If K has n vertices, we can think of its k-faces as sets of integers between 1 and n. A matrix chi is characteristic for K if all maximal minors of chi indexed by the facets of K have determinant equal to 1 or -1.

Authors

Version

This documentation describes version 1.0 of ToricTopology.

Source code

The source code from which this documentation is derived is in the file ToricTopology.m2.

Exports

  • Types
  • Functions and commands
  • Methods
    • bettiQTM(QuasiToricManifold), see bettiQTM -- Compute the betti numbers of a quasi-toric manifold
    • bettiQTM(ZZ,QuasiToricManifold), see bettiQTM -- Compute the betti numbers of a quasi-toric manifold
    • bettiSmallCover(SmallCover), see bettiSmallCover -- Compute the betti numbers of a small cover
    • bettiSmallCover(ZZ,SmallCover), see bettiSmallCover -- Compute the betti numbers of a small cover
    • chern(QuasiToricManifold), see chern -- Compute the Chern classes of a quasi-toric manifold
    • cohomologyRing(QuasiToricManifold), see cohomologyRing -- Compute the cohomology ring of a small cover or quasi-toric manifold
    • cohomologyRing(SmallCover), see cohomologyRing -- Compute the cohomology ring of a small cover or quasi-toric manifold
    • stiefelWhitney(SmallCover), see stiefelWhitney -- Compute the Stiefel-Whitney classes of a small cover
  • Symbols
    • QTMCharacteristicMatrix (missing documentation)
    • QTMDimension (missing documentation)
    • QTMSimplicialComplex (missing documentation)