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:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)