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RAAGs and Stable Commutator Length

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Nicolaus Heuer
University of Oxford
Fri, 01/02/2019 - 11:00 - 12:00
MPIM Lecture Hall

Stable commutator length ($\mathrm{scl}$) is a well established invariant of elements $g$ in the
commutator subgroup (write $\mathrm{scl}(g)$) and has both geometric and algebraic meaning.
Many classes of "non-positively curved" groups have a gap in stable commutator length: This is, for every non-trivial element $g$, $scl(g) > C$ for some $C > 0$. This gap may be thought of as an algebraic injectivity radius and can be found in hyperbolic groups, Baumslag-solitair groups, free products and Mapping Class Groups. However, the exact size of this gap usually unknown, which is due to a lack of a good source of quasimorphisms . In this talk I will construct a new source of quasimorphisms which yield optimal gaps and show that for Right-Angled
Artin Groups and their subgroups the gap of stable commutator length is exactly $1/2$.

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