Quasisymmetric functions from a topological point of view

Authors

  • Andrew Baker
  • Birgit Richter

DOI:

https://doi.org/10.7146/math.scand.a-15078

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.

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Published

2008-12-01

How to Cite

Baker, A., & Richter, B. (2008). Quasisymmetric functions from a topological point of view. MATHEMATICA SCANDINAVICA, 103(2), 208–242. https://doi.org/10.7146/math.scand.a-15078

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Articles