论文标题
代数拓扑中的重新归一化类固醇
Renormalization groupoids in algebraic topology
论文作者
论文摘要
Continuing work begin in arXiv:1910.12609, we interpret the Hurewicz homomorphism for Baker and Richter's noncommutative complex cobordism spectrum $Mξ$ in terms of characteristic numbers (indexed by quasi-symmetric functions) for complex-oriented quasitoric manifolds, and show that automorphisms or cohomology operations on this representation are defined by a非交通型线的形式差异性的“重归其化” HOPF代数，以前认为（超过$ q $）的量子电动力学。所得的结构可以纯粹的代数项表示，这是由该HOPF代数在非公共对称函数的环上定义的$ z $的群体方案。我们将一些应用绘制为符合性的复曲面歧管，简单球的组合和统计力学。
Continuing work begin in arXiv:1910.12609, we interpret the Hurewicz homomorphism for Baker and Richter's noncommutative complex cobordism spectrum $Mξ$ in terms of characteristic numbers (indexed by quasi-symmetric functions) for complex-oriented quasitoric manifolds, and show that automorphisms or cohomology operations on this representation are defined by a `renormalization' Hopf algebra of formal diffeomorphisms at the origin of the noncommutative line, previously considered (over $Q$) in quantum electrodynamics. The resulting structure can be presented in purely algebraic terms, as a groupoid scheme over $Z$ defined by a coaction of this Hopf algebra on the ring of noncommutative symmetric functions. We sketch some applications to symplectic toric manifolds, combinatorics of simplicial spheres, and statistical mechanics.
