论文标题
界限理论中的leray定理
Leray theorems in bounded cohomology theory
论文作者
论文摘要
该论文专门介绍了作者在有限的共同体学理论中涵盖定理方法的广义和简化版本。舒适性假设被较弱，更自然的无环假设所取代。在开放覆盖的情况下，去除了副型假设。结果表明，对于副型空间，如果相关的空间和子空间对基本组和覆盖空间的表现很好，则可以将封闭覆盖物的情况减少到开放覆盖的情况下。另一个覆盖封面定理的封面定理对单数同源性的行为很好。现在，只有它的证明使用捆绑理论。该方法也适用于$ L_1 $ - 样本。博览会在很大程度上是独立的。特别是，带有副型空间理论的所需结果提供了完整的证据。
The paper is devoted to a generalized and simplified version of author's approach to covering theorems in bounded cohomology theory. The amenability assumptions are replaced by weaker and more natural acyclicity assumprions. In the case of open coverings the paracompactness assumption is removed. It is shown that for paracompact spaces the case of closed coverings can be reduced to the case of open coverings if spaces and subspaces in question behave nicely with respect to fundamental groups and covering spaces. Another covering theorem for closed coverings assumes nice behavior with respect to singular homology; now only its proof uses the sheaf theory. The methods apply also to $l_1$-homology. The exposition is largely self-contained. In particular, the required results from the theory of paracompact spaces are presented with full proofs.
