Twisting Segal's K-homology theory
Twisting Segal's K-homology theory
复制标题
扭曲 Segal 的 K-同调理论
DOI：
10.1142/9789814425018_0007
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Dai Tamaki
中科院分区：
文献类型：
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作者：
Ibai Basabe;Jesus Gonzalez;Yuli Rudyak;and Dai Tamaki;山田裕一;山田裕一;Dai Tamaki
本文的目的是双重的：1。我们从同伦理论的角度快速地介绍了扭曲k理论，以及更一般的扭曲同调和上同调理论，以及2。我们构造了Segal的连接k -同调理论的一个扭曲版本。本文的前半部分是基于作者在“非交换几何和物理2008 - k -理论和d -膜-”会议上的演讲。扭转广义上同调理论的基本思想已经出现在Atiyah和Segal的论文[AS04]中，其中引入了扭曲k理论的现代处理。它们的构造是基于同伦理论的观点，即由表示谱的自同构扭曲的上同伦理论。目前代数拓扑学家把扭转（co）同调理论看作是由谱束定义的（co）同调理论。例如，参见CL Douglas [Dou06]。waldm<s:1> ller在[Wal]做了一个更系统的研究。本文的前半部分旨在为那些不熟悉同伦理论的人阐述扭曲（co）同伦理论的这些抽象方法背后的基本思想。
The aim of this article is twofold:1. we give a quick introduction to twisted K-theory and, more generally, twisted homology and cohomology theories from a homotopy theoretic point of view, and2. we construct a twisted version of Segal’s connective K-homology theory.The first half of this article is based on talks delivered by the author during the conference “Noncommutative Geometry and Physics 2008–K-theory and D-brane–”. The basic idea of twisting generalized cohomology theories already appeared in the paper [AS04] by Atiyah and Segal, in which a modern treatment of twisted K-theory was introduced. Their construction is based on a homotopy theoretic point of view, ie as cohomology theories twisted by automorphisms of representing spectra. Nowadays algebraic topologists regard twisted (co) homology theories as (co) homology theories defined by bundles of spectra. See, for example, CL Douglas [Dou06]. A more systematic study was done by Waldmüller in [Wal]. The first half of this article is intended to be an exposition of basic ideas behind these abstract approaches to twisted (co) homology theories for those who are not familiar with homotopy theory.