Admitting a Coarse Embedding is Not Preserved under Group Extensions

Goulnara Arzhantseva; Romain Tessera

doi:10.1093/imrn/rny017

Admitting a Coarse Embedding is Not Preserved under Group Extensions

Goulnara Arzhantseva
, Romain Tessera

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

Abstract

We construct a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite monster group: the first example of a finitely generated group that does not coarsely embed into Hilbert space and yet does not contain a weakly embedded expander.

Original language	English
Pages (from-to)	6480-6498
Number of pages	19
Journal	International Mathematics Research Notices
Volume	2019
Issue number	20
DOIs	https://doi.org/10.1093/imrn/rny017
Publication status	Published - 23 Oct 2019
Externally published	Yes

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title = "Admitting a Coarse Embedding is Not Preserved under Group Extensions",

abstract = "We construct a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite monster group: the first example of a finitely generated group that does not coarsely embed into Hilbert space and yet does not contain a weakly embedded expander.",

author = "Goulnara Arzhantseva and Romain Tessera",

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AU - Tessera, Romain

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PY - 2019/10/23

Y1 - 2019/10/23

N2 - We construct a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite monster group: the first example of a finitely generated group that does not coarsely embed into Hilbert space and yet does not contain a weakly embedded expander.

AB - We construct a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite monster group: the first example of a finitely generated group that does not coarsely embed into Hilbert space and yet does not contain a weakly embedded expander.

UR - https://www.scopus.com/pages/publications/85075178389

U2 - 10.1093/imrn/rny017

DO - 10.1093/imrn/rny017

M3 - Article

AN - SCOPUS:85075178389

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SP - 6480

EP - 6498

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 20

ER -

Admitting a Coarse Embedding is Not Preserved under Group Extensions

Abstract

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