论瞬子和单极浮子理论中的陶不变式

IF 0.8 2区数学 Q2 MATHEMATICS

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

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

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引用次数: 0

摘要

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。

On the tau invariants in instanton and monopole Floer theories

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On the tau invariants in instanton and monopole Floer theories

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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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.