论文标题
具有任意签名的Lefschetz纤维
Lefschetz fibrations with arbitrary signature
论文作者
论文摘要
我们开发技术，以在2个球员上构建显式符号Lefschetz纤维，并使用任何规定的签名和任何自旋类型在16中排除。这解决了对具有正签名的这种纤维的长期猜想。作为应用，我们产生同型同构但不是与S^2 x s^2的连接总和的差异的4个manifolds，迄今为止已知最小的拓扑，以及更大的示例作为符号lefschetz纤维。
We develop techniques to construct explicit symplectic Lefschetz fibrations over the 2-sphere with any prescribed signature and any spin type when the signature is divisible by 16. This solves a long-standing conjecture on the existence of such fibrations with positive signature. As applications, we produce symplectic 4-manifolds that are homeomorphic but not diffeomorphic to connected sums of S^2 x S^2, with the smallest topology known to date, as well as larger examples as symplectic Lefschetz fibrations.
