We give a topological description of the two-row Springer fiber over the real numbers. We show its cohomology ring coincides with the oddification of the cohomology ring of the complex Springer fiber introduced by Lauda–Russell. We also realize Ozsváth–Rasmussen–Szabó's odd TQFT from pullbacks and exceptional pushforwards along inclusion and projection maps between hypertori. Using these results, we construct the odd arc algebra as a convolution algebra over components of the real Springer fiber, giving an odd analog of a construction of Stroppel–Webster.

中文翻译：

---

真正的 Springer 纤维和奇弧代数

我们给出了实数上两排 Springer 光纤的拓扑描述。我们表明它的上同调环与劳达-罗素引入的复杂 Springer 纤维的上同调环的奇数化一致。我们还意识到 Ozsváth-Rasmussen-Szabó 奇怪的 TQFT 从回撤和沿着 hypertori 之间的包含和投影图的特殊推进。使用这些结果，我们将奇弧代数构造为真实 Springer 光纤分量上的卷积代数，给出了 Stroppel-Webster 构造的奇数模拟。