Singular chain: Difference between revisions
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==Definition== | ==Definition== | ||
A '''singular <math>n</math>-chain''' is defined as a formal linear combination of singular <math>n</math>-simplices, with integer coefficients. The set of all singular <math>n</math>-chains forms an Abelian group under coordinate-wise addition. This is in fact the free | A '''singular <math>n</math>-chain''' is defined as a formal linear combination of singular <math>n</math>-simplices (see [[defining ingredient::singular simplex]]), with integer coefficients. The set of all singular <math>n</math>-chains forms an Abelian group under coordinate-wise addition. This is in fact the free abelian group on the singular <math>n</math>-simplices, and is termed the <math>n^{th}</math> chain group. | ||
Latest revision as of 03:42, 23 December 2010
Definition
A singular -chain is defined as a formal linear combination of singular -simplices (see singular simplex), with integer coefficients. The set of all singular -chains forms an Abelian group under coordinate-wise addition. This is in fact the free abelian group on the singular -simplices, and is termed the chain group.
