Functorial semi-norms on singular homology and (in)flexible manifolds
Functorial semi-norms on singular homology and (in)flexible manifolds
复制标题
奇异同调和（内）柔性流形上的函数半范数
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
C. Loeh
中科院分区：
文献类型：
--
作者：
D. Crowley;C. Loeh
奇异同调上的泛函半范数是空间的奇异同调群上的半范数的集合，使得空间间的连续映射在同调上产生降范数映射。函数半范数可以用来给出有向流形之间映射的可能映射度的约束。在本文中，我们利用流形之间映射的度数信息来构造新的具有有趣性质的泛函半规范。特别地，我们通过提供在某些单连通空间的同调类上取有限正值的函子半范数来回答Gromov问题。我们的构造依赖于单连通流形的存在，这些单连通流形在某种意义上是不灵活的，因为它们所有的自映射都有度- 1,0或1。这种流形的存在首先是由Arkowitz和Lupton建立的；我们扩展他们的方法来生产各种各样的这样的流形。
A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing maps in homology. Functorial semi-norms can be used to give constraints on the possible mapping degrees of maps between oriented manifolds. In this paper, we use information about the degrees of maps between manifolds to construct new functorial semi-norms with interesting properties. In particular, we answer a question of Gromov by providing a functorial semi-norm that takes finite positive values on homology classes of certain simply connected spaces. Our construction relies on the existence of simply connected manifolds that are inflexible in the sense that all their self-maps have degree -1, 0, or 1. The existence of such manifolds was first established by Arkowitz and Lupton; we extend their methods to produce a wide variety of such manifolds.