# Topology/Exact Sequences

< Topology

An exact sequence is a tool used in Algebraic Topology used to extract information from a sequence of chain groups.

## DefinitionEdit

Given a sequence of groups and homomorphisms

is an exact sequence if for all , the sequence can be infinite.

Given an exact sequence of chain groups, with this indexing

we have a *chain complex*.

## Short Exact SequenceEdit

Given the special case where we have 3 groups with the following homomorphisms

where is a one-one homomorphism and is an onto homomorphism, we have a *short exact sequence*. Short exact sequences have the property .

## ExercisesEdit

(under construction)