Homological filling functions with coefficients

Groups, geometry, and dynamics

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