自旋4-流形的交形式与Pin（2）-等变Mahowald不变量
Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant
摘要：
在研究四维拓扑中地理问题的“11/8-猜想”时，古田提出了一个关于某些表示球面之间存在Pin（2）-等变稳定映射的问题。本文通过分析Pin（2）-等变Mahowald不变量，给出了该问题的一个完整解决方案.作为结果的几何应用，我们证明了一个“10/8+4”定理。我们通过分析由BPin（2）产生的有限谱和与之相关的各种Thom谱之间的映射来证明我们的定理，为了分析这些映射，我们使用了细胞图技术，球的稳定同伦群的已知结果，以及基于$j$的Atiyah-Hirzebruch谱序列.
英文摘要：
In studying the "11/8-Conjecture" on the Geography Problem in 4-dimensional topology, Furuta proposed a question on the existence of Pin(2)-equivariant stable maps between certain representation spheres. In this paper, we present a complete solution to this problem by analyzing the Pin(2)-equivariant Mahowald invariants. As a geometric application of our result, we prove a "10/8+4"-Theorem. We prove our theorem by analyzing maps between certain finite spectra arising from BPin(2) and various Thom spectra associated with it. To analyze these maps, we use the technique of cell diagrams, known results on the stable homotopy groups of spheres, and the $j$-based Atiyah-Hirzebruch spectral sequence.
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