标题： 不可压缩的填充流形 显示英文标题

标题： Incompressible fillings of manifolds

摘要： 我们找到了局部对称空间的Borel-Serre紧化边界的边界，其中任何填充都是不可压缩的。 我们通过证明这些边界具有小奇异模型，并利用这些模型来阻碍压缩。 我们还表明，边界的的小奇异模型阻碍了双曲填充内部的$S^1$-作用（以及更一般地同伦平凡的$\mathbb Z/p$-作用）。 我们利用这一点，根据基本群来限制这类内部上完整黎曼度量的对称性。 我们还使用小奇异模型来简化一些关于模空间的已知定理的证明（最小轨道空间定理和Royden定理的拓扑类比）。 显示英文摘要

摘要： We find boundaries of Borel-Serre compactifications of locally symmetric spaces, for which any filling is incompressible. We prove this result by showing that these boundaries have small singular models and using these models to obstruct compressions. We also show that small singular models of boundaries obstruct $S^1$-actions (and more generally homotopically trivial $\mathbb Z/p$-actions) on interiors of aspherical fillings. We use this to bound the symmetry of complete Riemannian metrics on such interiors in terms of the fundamental group. We also use small singular models to simplify the proofs of some already known theorems about moduli spaces (the minimal orbifold theorem and a topological analogue of Royden's theorem).