Department of Mathematics, University of California, Berkeley, CA 94720-3840
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10875-10879. doi: 10.1073/pnas.1717167115.
Building on work by Stallings, Jaco, and Hempel in three dimensions and a more recent four-dimensional analog by Abrams, Kirby, and Gay, we show how the splitting homomorphism and group trisection constructions can be extended to functors between appropriate categories. This further enhances the bridge between smooth four-dimensional topology and the group theory of free and surface groups.
基于 Stallings、Jaco 和 Hempel 在三维空间中的工作，以及 Abrams、Kirby 和 Gay 最近提出的更具创新性的四维类比，我们展示了如何将分裂同态和群三分结构扩展到适当范畴之间的函子。这进一步加强了光滑四维拓扑和自由群与曲面群的群论之间的桥梁。
