JP Journal of Algebra, Number Theory and Applications
Volume 28, Issue 1, Pages 1 - 12
(February 2013)
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PROPERTY (T) AND LEFT G-INVARIANT COARSE EMBEDDABILITY OF TOPOLOGICAL GROUPS
Tao Jicheng
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Abstract: Let Gbe a topological group with a left G-invariant metric dsatisfying We show that if Gadmits a left G-invariant coarse embedding into a Hilbert space, then Gdoes not have Property (T). As an application of our main results, we show that if Gand Hare two non-trivial countable discrete groups, which admit left G-invariant coarse embeddings into a Hilbert space and is their free product, then has not Property (T). |
Keywords and phrases: left G-invariant coarse embedding, Property (T), free product. |
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