【摘要】
Surface subgroups in hyperbolic 3-manifolds have fascinated mathematicians for decades for their intrinsic geometric beauty and far-reaching implications in low-dimensional topology, geometric group theory, and dynamics. In the proof of Surface Subgroup Theorem in 2009, Kahn and Markovic presented a powerful method to construct incompressible immersed surfaces in closed hyperbolic 3-manifolds, which is called "Good Panted Surfaces Construction." The surfaces made by this construction are ubiquitous and can be almost totally geodesic. Over the ensuing sixteen years to date, this technique has been gradually generalized and applied to build different kinds of surfaces in more locally symmetric spaces, e.g. in higher dimensional hyperbolic manifolds or cusped hyperbolic 3-manifold with finite volume, by Hamenstadt, Kahn-Wright, Kahn-Labourie-Mozes, and Kahn-Rao. In this mini-course, we will
-introduce the definitions concerning the good panted surface construction
-illustrate how to build incompressible surfaces out of good pants in dimension 3
-present the applications of this construction to closed hyperbolic n-manifolds
