Author:
Baker Andrew,Richter Birgit
Abstract
It is well-known that the homology of the classifying space of the unitary group is isomorphic to the ring of symmetric functions $\mathsf {Symm}$. We offer the cohomology of the space $\Omega \Sigma {\mathsf C} P^{\infty}$ as a topological model for the ring of quasisymmetric functions $\mathsf {QSymm}$. We exploit standard results from topology to shed light on some of the algebraic properties of $\mathsf {QSymm}$. In particular, we reprove the Ditters conjecture. We investigate a product on $\Omega \Sigma {\mathsf C} P^{\infty}$ that gives rise to an algebraic structure which generalizes the Witt vector structure in the cohomology of $BU$. The canonical Thom spectrum over $\Omega \Sigma {\mathsf C} P^{\infty}$ is highly non-commutative and we study some of its features, including the homology of its topological Hochschild homology spectrum.
Publisher
Det Kgl. Bibliotek/Royal Danish Library
Cited by
16 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献