We show that a spectral sequence developed by Lipshitz and Treumann, for application to Heegaard Floer theory, converges to a localized form of topological Hochschild homology with coefficients. This allows us to show that the target of this spectral sequence can be identified with Hochschild homology when the topological Hochschild homology is torsion-free as a module over ${THH}_{\ast }({\mathbb{F}}_2)$, parallel to results of Mathew on degeneration of the Hodge-to-de Rham spectral sequence.

中文翻译：

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展开相对的泰特对角线

我们展示了由 Lipshitz 和 Treumann 开发的用于 Heegaard Floer 理论的谱序列收敛到具有系数的拓扑 Hochschild 同源性的局部形式。这使我们能够证明，当拓扑 Hochschild 同源性作为一个模块无扭转时，可以使用 Hochschild 同源性识别该光谱序列的目标${THH}_{＊}({\mathbb{F}}_2)$，与 Mathew 关于 Hodge-to-de Rham 光谱序列退化的结果平行。