On the tau invariants in instanton and monopole Floer theories

Pub Date : 2024-06-05 DOI:10.1112/topo.12346

Sudipta Ghosh, Zhenkun Li, C.-M. Michael Wong

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Abstract

We unify two existing approaches to the tau invariants in instanton and monopole Floer theories, by identifying $τ_{G}$ , defined by the second author via the minus flavors ${\underset{̲}{KHI}}^{-}$ and ${\underset{̲}{KHM}}^{-}$ of the knot homologies, with $τ_{G}^{♯}$ , defined by Baldwin and Sivek via cobordism maps of the 3-manifold homologies induced by knot surgeries. We exhibit several consequences, including a relationship with Heegaard Floer theory, and use our result to compute ${\underset{̲}{KHI}}^{-}$ and ${\underset{̲}{KHM}}^{-}$ for twist knots.

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论瞬子和单极浮子理论中的陶不变式

我们将第二作者通过结同构的减味 KHI ̲ - $\underline{operatorname{KHI}}^-$ 和 KHM ̲ - $\underline{operatorname{KHM}}^-$ 定义的 τ G $\tau _\{mathrm{G}}$ 与 Baldwin 和 Sivek 通过共线性定义的 τ G ♯ $\tau \sharp _\{mathrm{G}}$ 统一为瞬子和单极浮子理论中的头不变式的两种现有方法、G τ ♯ $\tau ^\sharp _{mathrm{G}}$，由鲍德温和西韦克通过结手术诱导的 3-manifold同调的共线性映射定义。我们展示了几个结果，包括与 Heegaard Floer 理论的关系，并用我们的结果计算了扭结的 KHI ̲ - $\underline{\operatorname{KHI}}^-$ 和 KHM ̲ - $\underline{\operatorname{KHM}}^-$ 。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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