Title: Incompressible fillings of manifolds,
Abstract: 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).