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arXiv 2209.03548math.SG
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带边接触瞬子及其Fredholm理论与一般横截性

Bordered contact instantons and their Fredholm theory and generic transversalities

Yong-Geun Oh

备注：
v2) 41 pages;. application to Shelukhin's conjecture separated away to a separate paper with corrected proof, discussion on the mapping transversality in arXiv:2111.02957 moved to here, title and abstract changed, submitted for the proceedings for Bumsig Kim's Memorial conference. arXiv admin note: text overlap with arXiv:2205.00370 v3) 46 pages, typos corrected, final accepted version
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AI总结：

本文建立了带边接触瞬子的Fredholm理论，证明了在Legendrian边界条件及CR近复结构扰动下的一般横截性，为构造其模空间奠定基础。

摘要：

本文首先建立了带边接触瞬子的Fredholm理论，这些瞬子定义在带有边界穿刺附近指定渐近条件的穿刺黎曼曲面上。然后，我们证明了在Legendrian边界条件扰动下的一般映射横截性。我们还建立了在CR近复结构和Legendrian边界条件扰动下，其模空间的一般（0-jet）评估横截性结果。这些是构造带边接触瞬子模空间及其应用的基本要素。

英文摘要：

In this article, we first establish the Fredholm theory for the bordered contact instantons defined on the punctured Riemann surfaces with prescribed asymptotic condition near the boundary punctures. We then prove the generic mapping transversality under the perturbation of Legendrian boundary condition. We also establish their generic (0-jet) evaluation transversality results of their moduli space under the perturbations of CR almost complex structures and of Legendrian boundary conditions. These are fundamental ingredients of the construction of the moduli space of bordered contact instantons and their applications.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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