Quasisymmetric functions from a topological point of view

Baker, A. and Richter, B. (2008) Quasisymmetric functions from a topological point of view. Mathematica Scandinavica, 103(2), pp. 208-242.

Abstract

It is well-known that the homology of the classifying space of the unitary group is isomorphic to the ring of symmetric functions, Symm. 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, QSymm. We exploit standard results from topology to shed light on some of the algebraic properties of QSymm. In particular, we reprove the Ditters conjecture. We investigate a product on the loop space that gives rise to an algebraic structure which generalizes the Witt vector structure in the cohomology of BU. The canonical Thom spectrum over the loops on the suspension of BU(1) is highly non-commutative and we study some of its features, including the homology of its topological Hochschild homology spectrum.

• Item Type: Articles
• Keywords: James construction, quasisymmetric functions, Hilton-Milnor theorem, Thom spectra, Witt vectors
• Status: Published
• Refereed: No
• Glasgow Author(s) Enlighten ID: Baker, Dr Andrew
• Authors: Baker, A., and Richter, B.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Research Group: Algebraic topology
• Journal Name: Mathematica Scandinavica
• Journal Abbr.: Math. Scand,
• ISSN: 0025-5521

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