Goulnara N. Arzhantseva

Metrics on diagram groups and uniform embeddings in a Hilbert space

We give first examples of finitely generated groups having an intermediate, with values in

Coarse Non-Amenability and Coarse Embeddings

(0,1)

Compression functions of uniform embeddings of groups into Hilbert and Banach spaces

, Hilbert space compression (which is a numerical parameter measuring the distortion required to embed a metric space into Hilbert space). These groups include certain diagram groups. In particular, we show that the Hilbert space compression of Richard Thompsons group

A property of subgroups of infinite index in a free group

F

Solvable groups with polynomial Dehn functions

is equal to

Almost commuting permutations are near commuting permutations

1/2

Infinite groups with fixed point properties

, the Hilbert space compression of

A lower bound on the growth of word hyperbolic groups

\mathbb{Z}\wr\mathbb{Z}

Growth rates of amenable groups

is between

Admitting a Coarse Embedding is Not Preserved Under Group Extensions

1/2