Rational orthogonal calculus

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2017-04-13 DOI:10.1007/s40062-017-0172-4

David Barnes

引用次数: 2

Abstract

We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the rational homology type of the input functor, whose layers are given by rational spectra with an action of O(n). By work of Greenlees and Shipley, we see that these layers are classified by torsion \({{\mathrm{H}}}^*({{\mathrm{B}}}SO(n))[O(n)/SO(n)]\)-modules.

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有理正交演算

我们证明了可以用模型范畴来构造有理正交演算。也就是说，给定一个从向量空间到基空间的连续函子，人们可以仅依赖输入函子的有理同调类型来构造该函子的近似塔，其层由作用为O(n)的有理谱给出。通过Greenlees和Shipley的工作，我们看到这些层是通过扭转\({{\mathrm{H}}}^*({{\mathrm{B}}}SO(n))[O(n)/SO(n)]\) -模块分类的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

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