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Distinguishing Filling Invariants Associated to Conjugacy in Groups

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arxiv 2506.19264 v1 pith:L3VMG5HU submitted 2025-06-24 math.GR

Conan Gillis , Timothy Riley This is my paper · ORCID
classification math.GR
keywords groupsconjugacydehnfunctionfunctionsinvariantsthreeannular
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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.

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  1. Conjugator length in finitely presented groups

    math.GR 2026-07 accept novelty 6.0 of 10

    The conjugator length function is quadratic for the integral Heisenberg group and Stallings' group, and cyclic-subgroup distortion can be promoted to conjugator length.

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