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 Sequence: Definition, Example, Special Cases, Facts, Applications of Exact Sequences

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

... 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 ...

**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 ...

**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) ...

**Exact Sequence**s

... 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 ...

**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)