Definition
If X is a CW-complex with n-skeleton Xn, the cellular homology modules are defined as the homology groups of the cellular chain complex
The group
is free, with generators which can be identified with the n-cells of X. Let be an n-cell of X, let be the attaching map, and consider the composite maps
where is an -cell of X and the second map is the quotient map identifying to a point.
The boundary map
is then given by the formula
where is the degree of and the sum is taken over all -cells of X, considered as generators of .
Read more about this topic: Cellular Homology
Famous quotes containing the word definition:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)