论文标题
反身同源性
Reflexive homology
论文作者
论文摘要
反射性同源性是与反身交叉简单组相关的同源理论。基本交叉的简单组之一。这是扩展Hochschild同源性来检测订单反向的最通用的方法。在本文中，我们研究了自反循环空间的反射性同源性与$ C_2 $ Equivariant同源性之间的关系。我们从函子同源性方面定义了反射性同源性。我们给出了一个用于计算反身同源性的双色复合物以及一些计算，包括张量代数的反射性同源性。我们证明，组代数的反身同源性与分类空间的自由环空间上的$ c_2 $ equivariant borel构造的同源性同构。我们对组元素的共轭类索引的组代数的反射性同源性进行了直接的总和分解，在该类别元素的共轭类别中，汇总是根据组同源性的反射性类似物来定义的。我们定义了反射性同源性的越来越多的版本，并使用它来研究某些自由环和免费环路悬浮空间的$ C_2 $ Equivariant同源性。我们表明，反身同源性满足了莫里塔的不变性。我们证明，在良好的条件下，布劳恩（Braun）和fernàndez-valència和giansiracusa研究的参与hochschild同源性与反射性同源性相吻合。
Reflexive homology is the homology theory associated to the reflexive crossed simplicial group; one of the fundamental crossed simplicial groups. It is the most general way to extend Hochschild homology to detect an order-reversing involution. In this paper we study the relationship between reflexive homology and the $C_2$-equivariant homology of free loop spaces. We define reflexive homology in terms of functor homology. We give a bicomplex for computing reflexive homology together with some calculations, including the reflexive homology of a tensor algebra. We prove that the reflexive homology of a group algebra is isomorphic to the homology of the $C_2$-equivariant Borel construction on the free loop space of the classifying space. We give a direct sum decomposition of the reflexive homology of a group algebra indexed by conjugacy classes of group elements, where the summands are defined in terms of a reflexive analogue of group homology. We define a hyperhomology version of reflexive homology and use it to study the $C_2$-equivariant homology of certain free loop and free loop-suspension spaces. We show that reflexive homology satisfies Morita invariance. We prove that under nice conditions the involutive Hochschild homology studied by Braun and by Fernàndez-València and Giansiracusa coincides with reflexive homology.
