Groups, geometry, and dynamics | |
Homological filling functions with coefficients | |
article | |
Xingzhe Li1  Fedor Manin1  | |
[1] University of California;Cornell University | |
关键词: Homological filling functions; isoperimetric functions; Dehn functions; discrete Morse theory; | |
DOI : 10.4171/ggd/675 | |
学科分类:神经科学 | |
来源: European Mathematical Society | |
【 摘 要 】
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 RRR. Our main theorem is that the coefficients make a difference. That is, for every n≥1n \geq 1n≥1 and every pair of coefficient groups A,B∈{Z,Q}∪{Z/pZ :p prime}A, B \in \{\mathbb{Z},\mathbb{Q}\} \cup \{\mathbb{Z}/p\mathbb{Z}\colon p\text{ prime}\}A,B∈{Z,Q}∪{Z/pZ:p prime}, there is a group whose filling functions for nnn-cycles with coefficients in AAA and BBB have different asymptotic behavior.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO202307150000608ZK.pdf | 322KB | download |