Automorphisms of contact graphs of CAT(0) cube complexes

Fioravanti, Elia

doi:10.1093/imrn/rnaa280

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Automorphisms of contact graphs of CAT(0) cube complexes

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Fioravanti, Elia
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1093/imrn/rnaa280
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https://doi.org/10.48550/arXiv.2001.08493
(Preprint)

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Fioravanti_Automorphisms of Contact Graphs of CAT(0) Cube Complexes_2022.pdf
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Citation

Fioravanti, E. (2022). Automorphisms of contact graphs of CAT(0) cube complexes. International Mathematics Research Notices, 2022(5), 3278-3296. doi:10.1093/imrn/rnaa280.

Cite as: https://hdl.handle.net/21.11116/0000-0008-BCA6-9

Abstract

We show that, under weak assumptions, the automorphism group of a ${\rm
CAT(0)}$ cube complex $X$ coincides with the automorphism group of Hagen's
contact graph $\mathcal{C}(X)$. The result holds, in particular, for universal
covers of Salvetti complexes, where it provides an analogue of Ivanov's theorem
on curve graphs of non-sporadic surfaces. This highlights a contrast between
contact graphs and Kim-Koberda extension graphs, which have much larger
automorphism group. We also study contact graphs associated to Davis complexes
of right-angled Coxeter groups. We show that these contact graphs are less
well-behaved and describe exactly when they have more automorphisms than the
universal cover of the Davis complex.