In mathematics, the plus construction is a method for simplifying the fundamental group of a space without changing its homology and cohomology groupss.

is a based connected CW complex is a perfect normal subgroup.

The plus construction was introduced by , and was used by Daniel Quillen to define algebraic K-theory. Given a perfect normal subgroup of the fundamental group of a connected CW complex whose images in the fundamental group generate the subgroup. This operation generally changes the homology of the space, but these changes can be reversed by the addition of three-cells.

is a unital ring the group of invertible matricess elsewhere. The direct limit and its classifying space, generated by matrices which only differ from the identity matrix-th homotopy group, that is,

See also

• Semi-s-cobordism

References

• .

• .

• .

External links