In mathematics, homological stability is any of a number of theorems asserting that the group homology of a series of groups
Contents
is independent of n when n is large enough (depending on i). The smallest n such that the maps
Examples
Examples of such groups include the following:
Applications
In some cases, the homology of the group
can be computed by other means or is related to other data. For example, the Barratt–Priddy theorem relates the homology of the infinite symmetric group agrees with mapping spaces of spheres. This can also be stated as a relation between the plus construction of