论文标题
4个manifolds的稳定差异组
Stable diffeomorphism groups of 4-manifolds
论文作者
论文摘要
通过与选择的N-manifold Y正式反转连接的总和构造来引入N-manifolds类别的定位。在自多态组的水平上，这导致N-manifolds的稳定差异群。在维度为0和2中，这连接到了球体的稳定同型组和稳定的Riemann表面映射类组。在维度4中，n-manifold y可以选择许多本质上不同的候选者。结果表明，在情况下，bauer-furuta不变性在y = cp^2的情况下提供了不变性，这与复杂表面的birational分类有关。仅在目标类别本地化之后，其他Y才是这种情况。在这种情况下，可以表明K3稳定的鲍尔 - 毛状不变式确定s^2xs^2稳定不变性。
A localisation of the category of n-manifolds is introduced by formally inverting the connected sum construction with a chosen n-manifold Y. On the level of automorphism groups, this leads to the stable diffeomorphism groups of n-manifolds. In dimensions 0 and 2, this is connected to the stable homotopy groups of spheres and the stable mapping class groups of Riemann surfaces. In dimension 4 there are many essentially different candidates for the n-manifold Y to choose from. It is shown that the Bauer--Furuta invariants provide invariants in the case Y = CP^2, which is related to the birational classification of complex surfaces. This will be the case for other Y only after localisation of the target category. In this context, it is shown that the K3-stable Bauer--Furuta invariants determine the S^2xS^2-stable invariants.
