论文标题
关于弦拓扑中的科恩·琼斯同构
On Cohen-Jones isomorphism in string topology
论文作者
论文摘要
循环产品是字符串拓扑中的操作。 Cohen and Jones将LOOP产品的理论实现作为歧管$ M $的经典环频谱$ LM^{ - TM} $。使用此情况，他们提供了以下陈述的证明，即循环产品与Hochschild cohomology上的Gerstenhaber Cup产品同构$ HH^**（C^*（M）\，; C^*（M）$简单地连接$ M $。但是，在技术上很难证明他们的某些部分是合理的。本文的主要目的是对证明的几何部分进行详细的修改。为此，我们设置了McClure-Smith的Cosimimplicial产品的“最高较高同型”版本。我们证明了对称光谱类别中的Cohen-Jones同构的结构化版本。
The loop product is an operation in string topology. Cohen and Jones gave a homotopy theoretic realization of the loop product as a classical ring spectrum $LM^{-TM}$ for a manifold $M$. Using this, they presented a proof of the statement that the loop product is isomorphic to the Gerstenhaber cup product on the Hochschild cohomology $HH^*(C^*(M)\,;C^*(M))$ for simply connected $M$. However, some parts of their proof are technically difficult to justify. The main aim of the present paper is to give detailed modification to a geometric part of their proof. To do so, we set up an "up to higher homotopy" version of McClure-Smith's cosimplicial product. We prove a structured version of Cohen-Jones isomorphism in the category of symmetric spectra.
