标题： 关于具有全旗纤维的GKM纤维丛与实现性问题 显示英文标题

标题： On GKM fiber bundles and realizability with full flag fibers

摘要： 我们研究了在什么条件下，一个具有基空间、全空间和纤维均为GKM流形的等变纤维丛会诱导出相应GKM图的纤维化或纤维丛。特别是，我们给出了几个反例。至于逆向问题，即GKM图纤维丛的实现问题，我们将注意力集中在纤维方向上带有符号的GKM纤维丛上，这些纤维丛定义在 $n$-多边形上，且其纤维是全旗流形的GKM图。虽然已知这种纤维丛对于 $\mathbb{CP}^1$-纤维是可实现的，但我们观察到在更高维度下，实现性依赖于GKM纤维丛的扭曲自同构。我们分类了可能的扭曲同构，并证明可以通过我们的分类来决定实现性。 显示英文摘要

摘要： We investigate under which conditions an equivariant fiber bundle whose base, total space and fiber are GKM manifolds induces a fibration or fiber bundle of the corresponding GKM graphs. In particular, we give several counterexamples. Concerning the converse direction, i.e., the realization problem for fiber bundles of GKM graphs, we restrict to the setting of fiberwise signed GKM fiber bundles over $n$-gons whose fiber is the GKM graph of a full flag manifold. While it was known that any such bundle is realizable for a $\mathbb{CP}^1$-fiber, we observe that new phenomena occur in higher dimensions where realizability depends on the twist automorphism of the GKM fiber bundle. We classify possible twist isomorphsims and show that realizability can be decided in terms of our classification.