Open 𝑟-Spin Theory I: Foundations
Open 𝑟-Spin Theory I: Foundations
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DOI：
10.1093/imrn/rnaa345
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发表时间：
2021-02
影响因子：
1
通讯作者：
A. Buryak;E. Clader;Ran J. Tessler
中科院分区：
文献类型：
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作者：
A. Buryak;E. Clader;Ran J. Tessler
我们为具有边界的黎曼曲面的亏格为零的$r$-自旋理论奠定了基础。特别地，我们定义了$r$-自旋盘、它的模空间和Witten丛的概念，证明了模空间是一个紧致的光滑可定向的带角点的欧氏空间，并且证明了Witten丛相对于模空间是典型的相对定向的。在本文的续篇中，我们使用这些结构定义了开$r$-自旋交集理论，并将其与Gelfand-Dickey族联系起来，从而提供了Witten在开环境下的$r$-自旋猜想的模拟。
We lay the foundation for a version of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $r$-spin disks, their moduli space, and the Witten bundle; we show that the moduli space is a compact smooth orientable orbifold with corners, and we prove that the Witten bundle is canonically relatively oriented relative to the moduli space. In the sequel to this paper, we use these constructions to define open $r$-spin intersection theory and relate it to the Gelfand–Dickey hierarchy, thus providing an analog of Witten’s $r$-spin conjecture in the open setting.