We give an algorithm to compute the integer cohomology groups of any real partial flag manifold, by computing the incidence coefficients of the Schubert cells. For even flag manifolds we determine the integer cohomology groups, by proving that any torsion class has order 2 (generalizing a result of Ehresmann). We conjecture that this holds for any real flag manifold. We obtain results concerning which Schubert varieties represent integer cohomology classes, their structure constants and how to express them in terms of characteristic classes. For even flag manifolds and Grassmannians we also describe Schubert calculus. The Schubert calculus can be used to obtain lower bounds for certain real enumerative geometry problems (Schubert problems).

通过计算舒伯特单元的关联系数，我们给出了计算任何实部分标志流形的整数上同调群的算法。对于偶数标志流形，我们通过证明任何扭转类具有阶 2（推广 Ehresmann 的结果）来确定整数上同调群。我们推测这适用于任何真实的标志流形。我们获得了关于哪些舒伯特变体代表整数上同调类、它们的结构常数以及如何用特征类来表达它们的结果。甚至对于标志流形和格拉斯曼学派，我们也描述了舒伯特演算。舒伯特演算可用于获得某些实枚举几何问题（舒伯特问题）的下界。