Open Access
Translator Disclaimer
September 2020 Small cancellation labellings of some infinite graphs and applications
Damian Osajda
Author Affiliations +
Acta Math. 225(1): 159-191 (September 2020). DOI: 10.4310/ACTA.2020.v225.n1.a3

Abstract

We construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree. We use them to define infinite graphical small cancellation presentations of groups. This technique allows us to provide examples of groups with exotic properties:

• We construct the first examples of finitely generated coarsely non-amenable groups (that is, groups without Guoliang Yu’s Property A) that are coarsely embeddable into a Hilbert space. Moreover, our groups act properly on CAT(0) cubical complexes.

• We construct the first examples of finitely generated groups, with expanders embedded isometrically into their Cayley graphs—in contrast, in the case of the Gromov monster expanders are not even coarsely embedded.

We present further applications.

Citation

Download Citation

Damian Osajda. "Small cancellation labellings of some infinite graphs and applications." Acta Math. 225 (1) 159 - 191, September 2020. https://doi.org/10.4310/ACTA.2020.v225.n1.a3

Information

Received: 3 February 2016; Revised: 8 September 2019; Published: September 2020
First available in Project Euclid: 16 January 2021

Digital Object Identifier: 10.4310/ACTA.2020.v225.n1.a3

Subjects:
Primary: 05C15 , 20F06 , 20F69 , 46B85

Keywords: CAT(0) cubical complex , Coarse embedding , Graph coloring , Property A , small cancellation

Rights: Copyright © 2020 Institut Mittag-Leffler

JOURNAL ARTICLE
33 PAGES


SHARE
Vol.225 • No. 1 • September 2020
Back to Top