4-球面的微分同胚、Cerf理论与Montesinos孪生对
Diffeomorphisms of the 4-sphere, Cerf theory and Montesinos twins
AI总结：
本文通过构造从$S^2 \ imes S^2$中2-球面环路群到4-球面光滑映射类群的满同态，并利用Montesinos孪生对上的扭转给出显式生成元，推进了对4-球面光滑映射类群的理解。
摘要：
更好地理解4-球面光滑映射类群的一种方法是，以支撑在子流形邻域中的显式微分同胚的形式给出一组生成元，这类似于曲面上的Dehn扭转。作为朝此方向迈出的一步，我们描述了一个从与$S^2 \ imes S^2$中的2-球面环路相关联的群到该光滑映射类群的满同态，讨论了该同态定义域的两个自然的、在某种意义下互补的子群，证明其中一个包含在核中，并为另一个的像给出了如上所述的生成元。这些生成元被描述为沿Montesinos孪生对的扭转，即4-球面中在两点处横截相交的嵌入2-球面对。
英文摘要：
One way to better understand the smooth mapping class group of the 4-sphere would be to give a list of generators in the form of explicit diffeomorphisms supported in neighborhoods of submanifolds, in analogy with Dehn twists on surfaces. As a step in this direction, we describe a surjective homomorphism from a group associated to loops of 2-spheres in $S^2 \times S^2$'s onto this smooth mapping class group, discuss two natural and in some sense complementary subgroups of the domain of this homomomorphism, show that one is in the kernel, and give generators as above for the image of the other. These generators are described as twists along Montesinos twins, i.e. pairs of embedded 2-spheres in the 4-sphere intersecting transversely at two points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
