AI 中文总结
研究格拉斯曼流形\(gr(2,k)\)中一般点环面轨道的非平凡奇数维等变上同调，构造了有此类上同调的环面簇，还表明对小例子能用\(\mathbb{Q}\)系数在\(H^3_T\)中明确计算等变上同调。
AI 中文摘要
文献中存在奇数等变上同调的例子，但通常处于一度且仅用于表明奇数等变上同调可以存在。本文构造了一族环面簇，它们具有非平凡奇数等变上同调，在许多奇数度上作为格拉斯曼流形中一般点的环面轨道出现。然后表明对于小例子可以用\(\mathbb{Q}\)系数在\(H^3_T\)中明确计算等变上同调。
英文摘要
Examples of odd equivariant cohomology exist in the literature, but they are generally in degree one and used to show only that odd equivariant cohomology can exist. This paper produces a family of toric varieties which have non trivial odd equivariant cohomology which arise as torus orbits of generic points in the grassmannian in many odd degrees. We then show that is it is possible to compute the equivariant cohomology explicitly with \mathbb{Q}-coefficients in H^3_T for small examples.
