Journal article

Poincaré profiles of groups and spaces

Abstract:: We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincaré profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by Benjamini–Schramm–Timár. In this paper we focus on properties of the Poincaré profiles of groups with polynomial growth, and of hyperbolic spaces, where we deduce a connection between these profiles and conformal dimension. As applications, we use these invariants to show the non-existence of coarse embeddings in a variety of examples.

Publication status:: Published

Peer review status:: Peer reviewed

Actions

Email

Email this record

Send the bibliographic details of this record to your email address.

Your Email
Please enter the email address that the record information will be sent to.

-
Your message (optional)
Please add any additional information to be included within the email.
Cite

Cite this record

APA Style

Hume, D., Mackay, J. M., & Tessera, R. (2020). Poincaré profiles of groups and spaces. Revista Matemática Iberoamericana, 36(6), 1835–1886.

MLA Style

Hume, D., et al. “Poincaré Profiles of Groups and Spaces.” Revista Matemática Iberoamericana, vol. 36, no. 6, European Mathematical Society, 2020, pp. 1835–86.

Chicago Style

Hume, D, JM Mackay, and R Tessera. 2020. “Poincaré Profiles of Groups and Spaces.” Revista Matemática Iberoamericana 36 (6): 1835–86.
Share
Print

Access Document

Files:: HumeMackayTessera.pdf

(Preview, Accepted manuscript, pdf, 627.7KB, Terms of use)

Publisher copy:: 10.4171/rmi/1184

Authors

+ Hume, D More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author
ORCID:: 0000-0003-2195-6071

+ Mackay, JM More by this author

Role:: Author

+ Tessera, R More by this author

Role:: Author

Publisher:: European Mathematical Society
Journal:: Revista Matemática Iberoamericana More from this journal
Volume:: 36
Issue:: 6
Pages:: 1835–1886
Publication date:: 2020-03-02
Acceptance date:: 2019-06-13
DOI:: 10.4171/rmi/1184
ISSN:: 0213-2230

Language:: English
Keywords:: Poincare inequality

coarse invariant

nilpotent groups

hyperbolic groups

expanders
Pubs id:: pubs:976317
UUID:: uuid:b55edc77-a621-488d-b927-537654552082
Local pid:: pubs:976317
Source identifiers:: 976317
Deposit date:: 2019-06-14

Terms of use

Copyright holder:: European Mathematical Society
Copyright date:: 2020
Rights statement:: © European Mathematical Society
Notes:: This is the accepted manuscript version of the article. The final version is available online from European Mathematical Society at: http://dx.doi.org/10.4171/rmi/1184

Licence:: Terms and Conditions of Use for Oxford University Research Archive

Views and Downloads

About views and downloads

If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP