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Stable commutator length on RAAGs

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The stable commutator length scl(g) of an element g in a group G measures the least complexity of a surface to “fill” g. Stable commutator length on non-abelian free groups is now fairly well understood but some questions remain open: Which rational numbers arise as scls? What is the distribution of scl for random elements? What is the gap for chains of scl? I will give a partial answer to all of these questions for right-angled Artin groups (RAAGs). If time permits, I will also show that computing scl in RAA Gs is (unlike in free groups) NP-hard. This is joint work with Lvzhou Chen.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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