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.

- Alexander I. Suciu <a.suciu@neu.edu>

- Types
- QuasiToricManifold -- the class of all quasi-toric manifolds
- SmallCover -- the class of all small covers

- Functions and commands
- bettiQTM -- Compute the betti numbers of a quasi-toric manifold
- bettiSmallCover -- Compute the betti numbers of a small cover
- chern -- Compute the Chern classes of a quasi-toric manifold
- cohomologyRing -- Compute the cohomology ring of a small cover or quasi-toric manifold
- complexProjectiveSpace -- Complex projective space of dimension n
- hessenbergVariety -- Hessenberg variety asscoiated to the n-permutahedron
- isValidChar -- Whether a matrix is characteristic for a simplicial complex
- quasiToricManifold -- Create a quasi-toric manifold
- realProjectiveSpace -- Real projective space of dimension n
- smallCover -- Create a small cover
- stiefelWhitney -- Compute the Stiefel-Whitney classes of a small cover

- 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)