紧致流形上格作用的连续向量
Continuous quotients for lattice actions on compact manifolds
摘要：
设G是SL（n，Z）中的有限指数子群，N > 4.设G连续作用在流形M上，其中基本群Z^n在开集上保持正测度。进一步假设G在H^1（M）上的诱导作用是非平凡的。我们证明了G存在一个有限指数子群G'和一个G'从M到n-环面的等变连续映射，它在基本群上诱导一个同构.在M的基本群覆盖到一个无挠生成的无挠的幂零群群上的情况下，我们证明了更一般的结果，提供了连续的幂零性。我们也给出了一些新的例子流形G行动的定理适用。
英文摘要：
Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts continuously on a manifold M, with fundamental group Z^n, preserving a measure that is positive on open sets. Further assume that the induced G action on H^1(M) is non-trivial. We show there exists a finite index subgroup G' of G and a G' equivariant continuous map from M to the n-torus that induces an isomorphism on fundamental groups. We prove more general results providing continuous quotients in cases where the fundamental group of M surjects onto a finitely generated torsion free nilpotent group. We also give some new examples of manifolds with G actions to which the theorems apply.
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