L_p-compression of wreath products and some related groups
Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016
Location: MSRI: Simons Auditorium
wreath product
Lp-compression
amenable groups
a-T-menability
fixed point properties
hyperbolic groups and generalizations
Banach space
group cohomology
expander graph
index theory
non-commutative geometry
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
43-XX - Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
46-XX - Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
14651
We show a formula relating the L_p-compression exponent of a group and its wreath product with a cyclic group for p in [1, 2]. The argument extends the Markov type method introduced by Naor and Peres. Using wreath product as ingredients, we construct finitely generated amenable groups with arbitrary prescribed L_p compression exponent in the interval [0,1]. This can be viewed as an elementary amenable analogue of a result of Arzhantseva, Drutu and Sapir. Joint with Jeremie Brieussel
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Zheng Notes
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14651
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14651.mp4
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