nLab Pontrjagin ring

Idea

The operations on an H-space $X$ equip its homology with the structure of ring. At least for ordinary homology this is known as the Pontrjagin ring $H_*(X)$ of $X$.

Properties

The homological version of the group completion theorem relates the Pontrjagin ring of a topological monoid $A$ to that of its group completion $\Omega B A$.

Related concepts

• homology of loop spaces

References

• Lev Pontrjagin, Homologies in compact Lie groups, Rec. Math. [Mat. Sbornik] N.S., 1939 Volume 6(48), Number 3, Pages 389–422 (mathnet:5835)

• William Browder, Homology Rings of Groups, American Journal of Mathematics, Vol. 90, No. 1 (Jan., 1968) (jstor:2373440)

See also

• Wikipedia, Pontryagin product