2019/07/31 by Föhn, Philip
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1907.13317
This paper presents a simplification of the main argument in "Effective quasimorphisms on right-angled Artin groups" by Fernós, Forester and Tao. Their article introduces a family of quasimorphisms on a certain class of groups (called RAAG-like) acting on CAT(0) cube complexes. They show that these have uniform defect of 12 and take the value of at least 1 on a chosen element. With the Bavard Duality they conclude that hyperbolic elements of RAAG-like groups have stable commutator length of at least 1/24. Their proof that the quasimorphisms take the value 1 is quite technical and relies on some tools they introduce: the essential characteristic set and equivariant Euclidean embeddings. Here it is shown that this is unnecessary and a much shorter proof is given. This was originally part of my master thesis "Stable commutator length gap in RAAG-like groups" supervised by Alessandra Iozzi at ETH Zürich.