Contents

cohomology

# Contents

## Idea

The homological version of what is called the group completion theorem (McDuff-Segal 76) relates the Pontrjagin ring of a topological monoid $A$ to that of its group completion $\Omega B A$.

## References

The original articles are

Alternative proof using a model category of bisimplicial sets:

Alternative formulation for the case of commutative topological monoids:

• Oscar Randal-Williams, Group-completion, local coefficient systems and perfection, Q. J. Math. 64 (2013), no. 3, 795–803.

• Simon Gritschacher, A remark on the group-completion theorem (arxiv:1709.02036)

Generalization to generalized homology represented by ring spectra and relation to the Quillen plus construction:

• Thomas Nikolaus, The group completion theorem via localizations of ring spectra, 2017 (pdf)

A proof based on Nikolaus’s proof was written up in

• Oscar Bendix Harr, Group completion is a completion, PDF.

Last revised on May 28, 2021 at 17:44:42. See the history of this page for a list of all contributions to it.