Surface Bundles in Topology, Algebraic Geometry, and Group Theory

Nick Salter, Bena Tshishiku
2020 Notices of the American Mathematical Society  
A surface is one of the most basic objects in topology, but the mathematics of surfaces spills out far beyond its source, penetrating deeply into fields as diverse as algebraic geometry, complex analysis, dynamics, hyperbolic geometry, geometric group theory, etc. In this article we focus on the mathematics of families of surfaces: surface bundles. While the basics belong to the study of fiber bundles, we hope to illustrate how the theory of surface bundles comes into close contact with a broad
more » ... ontact with a broad range of mathematical ideas. We focus here on connections with three areas-algebraic topology, algebraic geometry, and geometric group theory-and see how the notion of a surface bundle provides a meeting ground for these fields to interact in beautiful and unexpected ways. What is a surface bundle? A surface bundle is a fiber bundle ∶ → whose fiber is a 2-dimensional manifold
doi:10.1090/noti2016 fatcat:rdz42jl4pfgslhyys2bhthe44u