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Geometry of Infinitely Presented Small Cancellation Groups and Quasi-homomorphisms

  • Goulnara Arzhantseva (a1) and Cornelia Druţu (a2)
Abstract

We study the geometry of infinitely presented groups satisfying the small cancellation condition $C^{\prime }(1/8)$ , and introduce a standard decomposition (called the criss-cross decomposition) for the elements of such groups. Our method yields a direct construction of a linearly independent set of power continuum in the kernel of the comparison map between the bounded and the usual group cohomology in degree 2, without the use of free subgroups and extensions.

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The first author was supported in part by the ERC grant ANALYTIC no. 259527, and by the Swiss NSF, under Sinergia grant CRSI22-130435. The second author was supported in part by the EPSRC grant no. EP/K032208/1 entitled “Geometric and analytic aspects of infinite groups”, by the project ANR Blanc ANR-10-BLAN 0116, acronym GGAA, and by the LABEX CEMPI.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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