通过无球面流形实现闭链
Realisation of cycles by aspherical manifolds
AI总结：
本文为 Steenrod 闭链实现问题提出纯组合方法，证明任意拓扑空间的 n 维同调类可由实对称三对角矩阵同谱流形的有限叶覆盖像实现，且弧连通空间的同调类可由无球面流形的连续像实现。
摘要：
我们为 N. Steenrod 的闭链实现问题开发了一种全新的纯组合方法。我们证明了，任意拓扑空间的任意 n 维同调类均可由流形 M^n 上的有限叶覆盖的像以某种重数实现，其中 M^n 是实对称三对角 (n=1)x(n+1) 矩阵的同谱流形。特别地，任意弧连通拓扑空间的任意同调类均可由无球面流形的连续像实现。
英文摘要：
We develop a new purely combinatorial approach to N. Steenrod's problem on realisation of cycles. We prove that every n-dimensional homology class of every topological space can be realised with some multiplicity by an image of a finite-fold covering over the manifold M^n, where M^n is the isospectral manifold of real symmetric tridiagonal (n=1)x(n+1) matrices. In particular, every homology class of every arcwise connected topological space can be realised by a continuous image of an aspherical manifold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
