从拓扑观点看拟对称函数
Quasisymmetric functions from a topological point of view
摘要：
众所周知，酉群的分类空间的同调同构于对称函数环Symm。我们提供的上同调的闭路空间的悬挂的无限复射影空间作为一个拓扑模型的环的拟对称函数，QSymm。我们利用标准的拓扑结果来阐明QSymm的一些代数性质。特别地，我们重新证明了迪特猜想。我们调查的产品上的闭路空间，产生了一个代数结构，推广了维特向量结构的上同调的BU。BU（1）的悬挂环上的正则Thom谱是高度非交换的，我们研究了它的一些性质，包括拓扑霍赫希尔德同调谱的同调性.
英文摘要：
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.
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