论文标题
Dehn Twist和nielsen的实现问题4个manifolds
Dehn twists and the Nielsen realization problem for spin 4-manifolds
论文作者
论文摘要
我们证明，对于带有非零签名的封闭式平滑旋转4个manifold $ x $，大约$（+2）$ - 或$（2）$ - $ x $中的dehn twist对于任何有限订单订单差异差异不同时。特别是，我们对Dehn Twist的映射类别产生的每个组产生的尼尔森实现问题负面回答。我们还表明，拓扑类别中的尼尔森实现问题与平滑类别之间存在差异，该类别的$ k3 $和$ k3 $和$ s^{2} \ times s^{2} $之间存在差异。证明的主要成分是Y. Kato的10/8类型不平等，以进行互动和改进。
We prove that, for a closed oriented smooth spin 4-manifold $X$ with non-zero signature, the Dehn twist about a $(+2)$- or $(-2)$-sphere in $X$ is not homotopic to any finite order diffeomorphism. In particular, we negatively answer the Nielsen realization problem for each group generated by the mapping class of a Dehn twist. We also show that there is a discrepancy between the Nielsen realization problems in the topological category and smooth category for connected sums of copies of $K3$ and $S^{2} \times S^{2}$. The main ingredients of the proofs are Y. Kato's 10/8-type inequality for involutions and a refinement of it.
