发表机构
IIT Kanpur（坎普尔印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究广义Dold流形间非零Brouwer度映射的存在性，证明在底空间或纤维不同时大多不存在，并应用于建立上同调刚性。
AI 中文摘要
我们研究了在两个可定向、等维数的广义Dold流形（GDMs）之间是否存在非零Brouwer度数的映射，这些流形以复部分旗流形为纤维，纤维化于实射影空间之上。此处考虑的GDMs是通过球面与复部分旗流形乘积上的对合（在球面上反对称作用，在旗流形上复共轭作用）的轨道空间得到的。我们证明，当两个不同的GDMs的底实射影空间不同时，除一个例外情形外，不存在非零度数的映射。此外，当底实射影空间相同但纤维不同时，我们证明在大多数情况下不存在非零度数的映射，包括至少一个纤维不是Grassmann流形的情形。作为我们研究的应用，我们建立了球面与复或四元数部分旗流形乘积类别的上同调刚性。
英文摘要
We study the existence of maps of nonzero Brouwer degree between two orientable, equal-dimensional generalized Dold manifolds (GDMs) fibered by complex partial flag manifolds over real projective spaces. The GDMs considered here are obtained as orbit spaces of the diagonal involution on the product of a sphere and a complex partial flag manifold, acting antipodally on the sphere and by complex conjugation on the flag manifold. We show that no map of nonzero degree exists between two distinct GDMs when their base real projective spaces are different, except in one exceptional case. Furthermore, when the base real projective spaces coincide but fibers are distinct, we prove the nonexistence of maps of nonzero degree in most cases, including those in which at least one of the fibers is not a Grassmannian. As an application of our study, we establish cohomological rigidity for the class of products of a sphere with a complex or quaternionic partial flag manifold.
Comments20 pages. Comments are welcome
