Difference between revisions of "Fundamental cocycle"
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| + | $#A+1 = 9 n = 0 | ||
| + | $#C+1 = 9 : ~/encyclopedia/old_files/data/F042/F.0402170 Fundamental cocycle | ||
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| − | The cochain in | + | {{TEX|auto}} |
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| + | ''of a cellular space $ X $ | ||
| + | whose $ ( n - 1) $- | ||
| + | skeleton $ X ^ {n - 1 } $ | ||
| + | is a point $ x _ {0} $'' | ||
| + | |||
| + | The cochain in $ C ^ {n} ( X, \pi _ {n} ( X)) $ | ||
| + | whose value on the cell $ e _ {i} ^ {n} $ | ||
| + | is the element of $ \pi _ {n} ( X, x _ {0} ) $ | ||
| + | corresponding to the closure $ \overline{ {e _ {i} ^ {n} }}\; $. | ||
| + | The cohomology class of the fundamental cocycle is the [[Fundamental class|fundamental class]] of $ X $. | ||
Latest revision as of 19:40, 5 June 2020
of a cellular space $ X $
whose $ ( n - 1) $-
skeleton $ X ^ {n - 1 } $
is a point $ x _ {0} $
The cochain in $ C ^ {n} ( X, \pi _ {n} ( X)) $ whose value on the cell $ e _ {i} ^ {n} $ is the element of $ \pi _ {n} ( X, x _ {0} ) $ corresponding to the closure $ \overline{ {e _ {i} ^ {n} }}\; $. The cohomology class of the fundamental cocycle is the fundamental class of $ X $.
How to Cite This Entry:
Fundamental cocycle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fundamental_cocycle&oldid=47022
Fundamental cocycle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fundamental_cocycle&oldid=47022
This article was adapted from an original article by A.V. Khokhlov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article