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YCor
YCor
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Coarse embeddableembeddability into Hilbert space of residually finite groups

By definition a finitely generated group G is coarsecoarsely embedded into Hilbert space if there is a function $F: G\to \ell_2$, such that $\|F(g_n)-F(h_n)\|\to\infty$ iff $d(g_n,h_n)\to\infty$, where $d$ is word metric with respect to some generationgenerating set. Is it true, that residually finite groups are coarsecoarsely embeddable into Hilbert space?

Coarse embeddable into Hilbert space of residually finite groups

By definition a finitely generated group G is coarse embedded into Hilbert space if there is a function $F: G\to \ell_2$, such that $\|F(g_n)-F(h_n)\|\to\infty$ iff $d(g_n,h_n)\to\infty$ where $d$ is word metric with respect to some generation set. Is it true, that residually finite groups are coarse embeddable into Hilbert space?

Coarse embeddability into Hilbert space of residually finite groups

By definition a finitely generated group G is coarsely embedded into Hilbert space if there is a function $F: G\to \ell_2$, such that $\|F(g_n)-F(h_n)\|\to\infty$ iff $d(g_n,h_n)\to\infty$, where $d$ is word metric with respect to some generating set. Is it true that residually finite groups are coarsely embeddable into Hilbert space?

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Mogilevmedved
Mogilevmedved
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Coarse embeddable into Hilbert space of residually finite groups

By definition a finitely generated group G is coarse embedded into Hilbert space if there is a function $F: G\to \ell_2$, such that $\|F(g_n)-F(h_n)\|\to\infty$ iff $d(g_n,h_n)\to\infty$ where $d$ is word metric with respect to some generation set. Is it true, that residually finite groups are coarse embeddable into Hilbert space?