Geometry of infinitely presented small cancellation groups, Rapid Decay and quasi-homomorphisms

Author: 

Arzhantseva, G
Drutu, C

Publication Date: 

21 August 2018

Journal: 

Canadian Journal of Mathematics

Last Updated: 

2019-04-17T04:10:21.127+01:00

DOI: 

10.4153/CJM-2018-036-7

abstract: 

We study the geometry of infinitely presented groups satisfying the small
cancelation condition C'(1/8), and define a standard decomposition (called the
criss-cross decomposition) for the elements of such groups. We use it to prove
the Rapid Decay property for groups with the stronger small cancelation
property C'(1/10). As a consequence, the Metric Approximation Property holds
for the reduced C*-algebra and for the Fourier algebra of such groups. Our
method further implies that the kernel of the comparison map between the
bounded and the usual group cohomology in degree 2 has a basis of power
continuum. The present work can be viewed as a first non-trivial step towards a
systematic investigation of direct limits of hyperbolic groups.

Symplectic id: 

369814

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article