Homological and homotopical higher-order filling functions

TL;DR

This paper constructs specific groups demonstrating differences in higher-order filling functions, revealing complex behaviors and non-subrecursive growth in certain algebraic invariants.

Contribution

It introduces new groups where higher-order filling functions differ and exhibit non-subrecursive growth, advancing understanding of geometric group theory.

Findings

Existence of groups with FV^3(n) != ^2(n)

Construction of groups G_k with non-subrecursive ^k(n)

Demonstration of complex behaviors in higher-order filling functions

Abstract

We construct groups in which FV^3(n) != \delta^2(n). This construction also leads to groups G_k, k >= 3 for which \delta^{k}(n) is not subrecursive.