论文标题
具有系数的同源填充功能
Homological Filling Functions with Coefficients
论文作者
论文摘要
用无调的表面填充在Cayley图中填充环路有多困难？在“无限群体的渐近不变”中对格罗莫夫的评论后，我们定义了$ r $ $ r $系数的组的同源填充功能。我们的主要定理是系数有所不同。也就是说，对于每$ n \ geq 1 $和每对系数组$ a，b \ in \ {\ mathbb {z}}，\ sathbb {q} \} \ cup \} \ cup \ {\ mathbb {z}/p {z}/p \ mathb {z} $ n $ cycles含有$ a $和$ b $的系数具有不同的渐近行为。
How hard is it to fill a loop in a Cayley graph with an unoriented surface? Following a comment of Gromov in "Asymptotic invariants of infinite groups", we define homological filling functions of groups with coefficients in a group $R$. Our main theorem is that the coefficients make a difference. That is, for every $n \geq 1$ and every pair of coefficient groups $A, B \in \{\mathbb{Z},\mathbb{Q}\} \cup \{\mathbb{Z}/p\mathbb{Z} : p\text{ prime}\}$, there is a group whose filling functions for $n$-cycles with coefficients in $A$ and $B$ have different asymptotic behavior.
