Relative Commutant Pictures of Roe Algebras

Jan Spakula; Aaron Peter Tikuisis

doi:10.1007/s00220-019-03313-x

Relative Commutant Pictures of Roe Algebras

Jan Spakula, Aaron Peter Tikuisis^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

University of Southampton

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

36 Downloads (Pure)

Abstract

Let X be a proper metric space, which has finite asymptotic dimension in the sense of Gromov (or more generally, straight finite decomposition complexity of Dranishnikov and Zarichnyi). New descriptions are provided of the Roe algebra of X: (i) it consists exactly of operators which essentially commute with diagonal operators coming from Higson functions (that is, functions on X whose oscillation tends to 0 at ∞), and (ii) it consists exactly of quasi-local operators, that is, ones which have finite -propogation (in the sense of Roe) for every > 0. These descriptions hold both for the usual Roe algebra and for the uniform Roe algebra.

Original language	English
Pages (from-to)	1019-1048
Number of pages	30
Journal	Communications in Mathematical Physics
Volume	365
Issue number	3
Early online date	30 Jan 2019
DOIs	https://doi.org/10.1007/s00220-019-03313-x
Publication status	Published - Feb 2019

Bibliographical note

AT was supported by EPSRC EP/N00874X/1.
JS was supported by Marie Curie FP7-PEOPLE-2013-CIG Coarse Analysis (631945). We would like to thank Ulrich Bunke, Alexander Engel,
John Roe, Thomas Weighill, Stuart White, and Rufus Willett for comments and discussion relating to this piece.

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Accepted Manuscript
This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00220-019-03313-x
Accepted author manuscript, 430 KBLicence: Unspecified
Spakula_etal_sv_relative_commutant_AAM
This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00220-019-03313-x
Accepted author manuscript, 430 KB

Cite this

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Relative Commutant Pictures of Roe Algebras

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