论文标题
四维完整交集的平滑分类
The smooth classification of 4-dimensional complete intersections
论文作者
论文摘要
我们证明了关于4维完成交集的分类，以达到差异形态的分类。在这里，$ n $维的完整交叉点是一个平滑的复杂品种，由$ c $ hypersurfaces $ cp^{n+k} $的横向交叉点形成。 以前，克雷克和旅行证明了4维的沙利文猜想，当64分配了总学位（定义超曲面的学位的乘积）时，Fang and Klaus证明了该猜想的符合均匀拷贝8-Spheres $θ_8= Z/2 $的动作。 我们的证明涉及几个新想法，包括使用Hambleton-Madsen学位理论-D $普通地图，这些理论在各个方面都为Sullivan猜想提供了新的视角。这导致Segal猜想以$ S^1 $与Sullivan猜想之间的意外联系。
We prove the "Sullivan Conjecture" on the classification of 4-dimensional complete intersections up to diffeomorphism. Here an $n$-dimensional complete intersection is a smooth complex variety formed by the transverse intersection of $k$ hypersurfaces in $CP^{n+k}$. Previously Kreck and Traving proved the 4-dimensional Sullivan Conjecture when 64 divides the total degree (the product of the degrees of the defining hypersurfaces) and Fang and Klaus proved that the conjecture holds up to the action of the group of homotopy 8-spheres $Θ_8 = Z/2$. Our proof involves several new ideas, including the use of the Hambleton-Madsen theory of degree-$d$ normal maps, which provide a fresh perspective on the Sullivan Conjecture in all dimensions. This leads to an unexpected connection between the Segal Conjecture for $S^1$ and the Sullivan Conjecture.
