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CellComplex -- the class of all cell complexes

Description

A cell complex in this context is the combinatorial data of a CW-complex, i.e. a collection of cells in various dimensions along with their boundary expressed as a sequence of cells along with an orientation such that the boundary is a cycle.

Caveat

Not every object represented by a CellComplex object corresponds to a topological cell complex. In general there is no way to check that such a topological realization exists.

See also

Functions and methods returning a cell complex:

Methods that use a cell complex:

  • boundaryMap(ZZ,CellComplex) -- compute the boundary map of a cell complex from r-faces to (r-1)-faces
  • cells(CellComplex) -- see cells -- return the cells of a cell complex as a hashtable whose keys are cell dimensions
  • cells(ZZ,CellComplex) -- return the cells of a cell complex
  • complex(CellComplex) -- compute the cellular chain complex for a cell complex
  • dim(CellComplex) -- compute the dimension of a cell complex
  • facePoset(CellComplex) -- generates the face poset of a cell complex
  • HH CellComplex -- compute the homology modules of a cell complex
  • HH^ZZ CellComplex -- cohomology of a cell complex
  • HH_ZZ CellComplex -- compute the homology modules of a cell complex
  • isFree(CellComplex) -- checks if the labels of a cell complex are free modules
  • isMinimal(CellComplex) -- see isMinimal -- check if a labeled cell complex supports a minimal resolution
  • isWellDefined(CellComplex) -- checks if a cell complex is well defined
  • maxCells(CellComplex) -- see maxCells -- gives the maximal cells of a cell complex
  • net(CellComplex) (missing documentation)
  • relabelCellComplex(CellComplex,HashTable) -- see relabelCellComplex -- relabels a cell complex
  • ring(CellComplex) -- return the base ring of a cell complex
  • RingMap ** CellComplex -- tensors labels via a ring map
  • CellComplex _ List -- see subcomplex -- the subcomplex induced by a degree or monomial
  • CellComplex _ RingElement -- see subcomplex -- the subcomplex induced by a degree or monomial
  • CellComplex _ ZZ -- see subcomplex -- the subcomplex induced by a degree or monomial
  • subcomplex(CellComplex,List) -- see subcomplex -- the subcomplex induced by a degree or monomial
  • subcomplex(CellComplex,RingElement) -- see subcomplex -- the subcomplex induced by a degree or monomial
  • subcomplex(CellComplex,ZZ) -- see subcomplex -- the subcomplex induced by a degree or monomial

For the programmer

The object CellComplex is a type, with ancestor classes HashTable < Thing.


The source of this document is in CellularResolutions/doc.m2:43:0.