发表机构
Karlsruher Institut für Technologie（卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于分裂论证的新方法，证明非零单纯体积流形去除余维二子流形后基本群的有界上同调非零，并将补空间存在性转化为同调计算。
AI 中文摘要
在本文中，我们发展了一种证明有界上同调非零的新方法。该方法利用了一个分裂论证，其最简形式如下：设M为具有非零单纯体积的n维流形，N为M的余维二子流形，则可以得出M\N的基本群的n阶有界上同调非零。随后，我们将具有给定基本群的补空间的存在性转化为一个易于计算的同调计算，这可能具有独立的研究价值。
英文摘要
In this note we develop a novel approach for proving the non-vanishing of bounded cohomology. This utilizes a splitting argument whose simplest form is as follows: Let M denote an n-manifold of non-zero simplicial volume and N a codimension two submanifold of M, then one can conclude that the n-th bounded cohomology of the fundamental group of M \ N is non-zero. We then translate the existence of a complement with a given fundamental group into an easily accessible homology computation, which might be of independent interest.
CommentsThis paper represents a rework of the erroneous paper arXiv:2503.22511. It represents the attempts of the author to repair and further develop the approach of arXiv:2503.22511
