Relative expanders

Goulnara Arzhantseva; Romain Tessera

doi:10.1007/s00039-015-0316-9

Relative expanders

Goulnara Arzhantseva, Romain Tessera

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

Abstract

We exhibit a finitely generated group G and a sequence of finite index normal subgroups [InlineMediaObject not available: see fulltext.] such that for every finite generating subset S ⊆ G, the sequence of finite Cayley graphs (G/N_n, S) does not coarsely embed into any L^p-space for 1 ≤ p < ∞ (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander. The reason why our examples do not coarsely embed is a new phenomenon called relative expansion, which we define in terms of Poincaré inequalities.

Original language	English
Pages (from-to)	317-341
Number of pages	25
Journal	Geometric and Functional Analysis
Volume	25
Issue number	2
DOIs	https://doi.org/10.1007/s00039-015-0316-9
Publication status	Published - 1 Apr 2015
Externally published	Yes

Keywords

20E22
20F69
22D10
46B85

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10.1007/s00039-015-0316-9

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title = "Relative expanders",

abstract = "We exhibit a finitely generated group G and a sequence of finite index normal subgroups [InlineMediaObject not available: see fulltext.] such that for every finite generating subset S ⊆ G, the sequence of finite Cayley graphs (G/Nn, S) does not coarsely embed into any Lp-space for 1 ≤ p < ∞ (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander. The reason why our examples do not coarsely embed is a new phenomenon called relative expansion, which we define in terms of Poincar{\'e} inequalities.",

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AB - We exhibit a finitely generated group G and a sequence of finite index normal subgroups [InlineMediaObject not available: see fulltext.] such that for every finite generating subset S ⊆ G, the sequence of finite Cayley graphs (G/Nn, S) does not coarsely embed into any Lp-space for 1 ≤ p < ∞ (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander. The reason why our examples do not coarsely embed is a new phenomenon called relative expansion, which we define in terms of Poincaré inequalities.

KW - 20E22

KW - 20F69

KW - 22D10

KW - 46B85

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EP - 341

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 2

ER -

Relative expanders

Abstract

Keywords

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