Theorem shows free factor complex does not follow combinatorial isoperimetric inequality, suggesting implications for higher rank free groups.
We show that the free factor complex of the free group of rank n ≥ 4 n ≥ 4 does not satisfy a combinatorial isoperimetric inequality combinatorial isoperimetric inequality : that is, for every N ∈ N N ∈ N , there is a loop c N c_N of length 4 in the free factor complex such that the number of 2-simplices required to fill c N c_N grows at least as a linear function of N N . To prove the result, we construct a coarsely Lipschitz map from the ‘upward link’ of a free factor to Z Z .
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Radhika Gupta (2025) studied this question.
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