负曲流形的基本类不能用流形的乘积表示
Fundamental classes of negatively curved manifolds cannot be represented by products of manifolds
摘要：
不是每个奇异同调类都是某个流形的基本类的推进。在同样的精神，人们可以研究以下问题：哪些奇异同调类是给定类型流形的基本类的推进？在本文中，我们证明了负弯曲流形的基本类不能用流形的非平凡积来表示。这一发现对紧曲面的乘积给出的奇异同调的函子半范数有一定的启示。
英文摘要：
Not every singular homology class is the push-forward of the fundamental class of some manifold. In the same spirit, one can study the following problem: Which singular homology classes are the push-forward of the fundamental class of a given type of manifolds? In the present article, we show that the fundamental classes of negatively curved manifolds cannot be represented by a non-trivial product of manifolds. This observation sheds some light on the functorial semi-norm on singular homology given by products of compact surfaces.
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。
