Distinguishing Filling Invariants Associated to Conjugacy in Groups

TL;DR

This paper explores the relationships between annular Dehn functions, Dehn functions, and conjugator length functions in finitely generated groups, demonstrating their independence through diverse examples.

Contribution

It provides a comprehensive analysis showing that these three conjugacy invariants are mutually independent, with new examples illustrating this independence.

Findings

Annular Dehn functions, Dehn functions, and conjugator length functions are independent invariants.

Diverse group examples demonstrate the independence of these functions.

Theoretical relationships between these invariants are clarified.

Abstract

Brick and Corson introduced annular Dehn functions in 1998 to quantify the conjugacy problem for finitely generated groups and gave the fundamental relationships between it, the Dehn function, and the conjugator length function. We furnish the theory with diverse examples groups. In particular, we show that these three invariants are independent -- no two of the three functions determine the other.