2026-04-13T05:43:09Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/3775442024-12-20T13:58:36Zcom_2072_199267com_2072_4427col_2072_199862

Geometry of infinitely presented small cancellation groups, Rapid Decay and quasi-homomorphisms Arzhantseva, G. Drutu, C. We study the geometry of infinitely presented groups satisfying the small cancelation condition $ C'\''(1/8)$ , and define a standard decomposition (called the \dec decomposition) for the elements of such groups. We use it to prove the Rapid Decay property for groups $ G$ with the stronger small cancelation property $ C'\''(1/10)$ . As a consequence, the Metric Approximation Property holds for the reduced $ C^*$ --algebra $ C^*_r(G)$ and for the Fourier algebra $ A(G)$ of the group $ G$ . 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. 2020-10-14T11:18:57Z 2024-09-19T13:26:15Z 2020-10-14T11:18:57Z 2024-09-19T13:26:15Z 2020-10-14T11:18:57Z 2024-09-19T13:26:15Z 2014-01-01 info:eu-repo/semantics/preprint http://hdl.handle.net/2072/377544 eng CRM Preprints info:eu-repo/semantics/openAccess L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-nd/4.0/ RECERCAT (Dipòsit de la Recerca de Catalunya)