If is a cell space, then let be the cell complex where the -th group is the free abelian group on the cells of dimension , and the boundary map is as follows: If is an -cell, then we can define a map , where is any cell of dimension by the following rule: let be the attaching map for , where is the -skeleton of . Then let be the natural projection
Let . Now, is a (n-1)-sphere, so the map has a degree which we use to define the boundary operator:
The resulting chain complex is called the cellular chain complex.
|Date of creation||2013-03-22 13:14:55|
|Last modified on||2013-03-22 13:14:55|
|Last modified by||bwebste (988)|