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Complexes :: Making maps between chain complexes

Making maps between chain complexes -- information about the basic constructors

Basic constructors

Important computations creating new complex maps

  • resolutionMap(Complex) -- map from a free resolution to the given complex
  • HH ComplexMap (missing documentation)
  • augmentationMap(Complex) (missing documentation)
  • extend(Complex,Complex,Matrix) (missing documentation)

Canonical maps between complexes

Some complexes come with canonical maps. To access the complex map, one uses canonicalMap(Complex,Complex). The following operations have associated canonical maps.

Random maps of chain complexes

The method randomComplexMap(Complex,Complex) (missing documentation) allows one to construct random complex maps, random morphisms between complexes, and random null homotopies between complexes.

Elementary operations on complex maps

  • ComplexMap + ComplexMap (missing documentation)
  • ComplexMap | ComplexMap (missing documentation)
  • ComplexMap || ComplexMap (missing documentation)
  • ComplexMap ++ ComplexMap (missing documentation)
  • ComplexMap ** ComplexMap (missing documentation)
  • Hom(ComplexMap,ComplexMap) (missing documentation)
  • dual(ComplexMap) (missing documentation)
  • ComplexMap _ Array (missing documentation)
  • ComplexMap ^ Array (missing documentation)
  • naiveTruncation(ComplexMap,Sequence) (missing documentation)
  • canonicalTruncation(ComplexMap,Sequence) (missing documentation)
  • RingMap ComplexMap -- apply a ring map to a map of complexes
  • RingMap ** ComplexMap -- tensor a map of complexes along a ring map

See also