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Topology/Geometry Seminar

Stable commutator lengths of integral chains in right-angled Artin groups

Lvzhou Chen (UT Austin)

Location:  zoom link:
Date & time: Tuesday, 13 October 2020 at 3:50PM - 4:50PM

The stable commutator length (scl) is an invariant for group elements, and it carries topological and dynamical information. Topologically, an integral 1-chain in a group G is a formal sum of loops in the K(G,1) space, and its scl is the least complexity of surfaces bounding the union of these loops. Aiming for effective lower bounds of the index of special subgroups (say in hyperbolic 3-manifold groups), we give lower bounds for scl of integral chains in right-angled Artin groups (RAAGs) and right-angled Coxester groups (RACGs). We show that the infimal positive scl of integral chains in any RAAG/RACG is positive, and its size explicitly depends on the defining graph of the RAAG/RACG up to a multiplicative constant 12. In particular, the size is non-uniform among RAAGs/RACGs, but it is uniform among *hyperbolic* RACGs. If time permits, I will also explain a connection between scl in RAAGs and the so-called fractional stability number of graphs. This is joint work with Nicolaus Heuer.

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