## First Copenhagen Topology Conference## The University of Copenhagen## September 1-3 2006 |

It is well-known that the homology of the classifying space of the unitary group is isomorphic to the ring of symmetric functions. We offer the cohomology of the loop space of the suspension of the infinite complex projective space as a topological model for the ring of quasisymmetric functions. I'll explain how to exploit topology to reprove the Ditters conjecture which says that the ring of quasisymmetric functions is a polynomial ring.

The loop map to BU gives a canonical Thom spectrum over $\Omega\Sigma\mathbb{C}P^\infty$. This spectrum is highly non-commutative. I'll talk about the homology of its topological Hochschild homology spectrum.