# Exact Sequence

An exact sequence is a concept in mathematics, especially in ring and module theory, homological algebra, as well as in differential geometry and group theory. An exact sequence is a sequence, either finite or infinite, of objects and morphisms between them such that the image of one morphism equals the kernel of the next.

Read more about Exact SequenceDefinition, Example, Special Cases, Facts, Applications of Exact Sequences

### Other articles related to "exact sequence, sequence, exact, exact sequences, sequences":

Leray Cover
... Sheaf cohomology measures the extent to which a locally exact sequence on a fixed topological space, for instance the deRham sequence, fails to be globally exact ... Moreover, important properties, such as the existence of a long exact sequence in cohomology corresponding to any short exact sequence of sheaves, follow directly from the definition ...
Surgery Exact Sequence - Examples - 1. Homotopy Spheres
... The idea of the surgery exact sequence is implicitly present already in the original article of Kervaire and Milnor on the groups of homotopy spheres ... the cobordism group of almost framed manifolds, The surgery exact sequence in this case is an exact sequence of abelian groups ... we have Because the odd-dimensional L-groups are trivial one obtains these exact sequences The results of Kervaire and Milnor are obtained by studying the middle map in the first two sequences and ...
Five-term Exact Sequence
... In mathematics, five-term exact sequence or exact sequence of low-degree terms is a sequence of terms related to the first step of a spectral sequence ... More precisely, let E2p,q ⇒ H n(A) be a spectral sequence, whose terms are non-trivial only for p, q ≥ 0 ... Then there is an exact sequence 0 → E21,0 → H 1(A) → E20,1 → E22,0 → H 2(A) ...
Applications of Exact Sequences
... the theory of abelian categories, short exact sequences are often used as a convenient language to talk about sub- and factor objects ... Given the end terms A and C of a short exact sequence, what possibilities exist for the middle term B?" In the category of groups, this is equivalent to the question, what groups B ... Notice that in an exact sequence, the composition fi+1 fi maps Ai to 0 in Ai+2, so every exact sequence is a chain complex ...
Surgery Exact Sequence - The Exactness
... necessary to explain what is meant when talking about the "exact sequence" ... So the surgery exact sequence is an exact sequence in the following sense ...

### Famous quotes containing the words sequence and/or exact:

We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.
—E.M. (Edward Morgan)

Bid her paint till day of doom,
To this favour she must come.
Bid the merchant gather wealth,
The usurer exact by stealth,
The proud man beat it from his thought,
Yet to this shape all must be brought.
Francis Beaumont (1584-1616)