Let X be a simply connected space and K be any field. The normalized singular cochains N*(X; K) admit a natural strongly homotopy commutative algebra structure, which induces a natural product on the Hochschild homology HH* N*X of the space X. We prove that, endowed with this product, HH* N*X is isomorphic to the cohomology algebra of the free loop space of X with coefficients in K. We also show how to construct a simpler Hochschild complex which allows direct computation. (C) 2001 Elsevier Science Ltd. All rights reserved. [References: 30]
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机译：设X为简单连通的空间，而K为任意字段。归一化的奇异共链N *（X; K）接受自然的强同伦交换代数结构，该结构在空间X的Hochschild同源HH * N * X上诱导出天然乘积。我们证明，赋予该乘积的HH * N * X与X的自由循环空间的同调代数同构，其系数为K。我们还展示了如何构造更简单的Hochschild复数，该复数可以直接计算。 （C）2001 Elsevier ScienceLtd。保留所有权利。 [参考：30]
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