Infinitely presented graphical small cancellation groups
Event details
| Date | 04.02.2016 |
| Hour | 13:00 › 14:00 |
| Speaker | Dominik Gruber |
| Location | |
| Category | Conferences - Seminars |
Graphical small cancellation theory is a tool for constructing finitely generated groups with prescribed subgraphs embedded in their Cayley graphs. It has provided the only known counterexamples to the Baum-Connes conjecture with coefficients and the only known non-coarsely amenable groups.
I will present a purely combinatorial approach to the theory, which is more general and allows more flexibility than prior interpretations. I will explain that this approach produces groups with coarsely embedded prescribed infinite sequences of finite graphs. Therefore, it yields groups with the properties mentioned above. I will discuss that the resulting infinitely presented groups are acylindrically hyperbolic (joint work with A. Sisto). This generalization of the notion of Gromov hyperbolicity has strong analytic, algebraic, and geometric implications. The arguments rely on the Euler characteristic formula for planar 2-complexes and on a characterization of Gromov hyperbolic graphs through linear isoperimetric inequalities.
I will present a purely combinatorial approach to the theory, which is more general and allows more flexibility than prior interpretations. I will explain that this approach produces groups with coarsely embedded prescribed infinite sequences of finite graphs. Therefore, it yields groups with the properties mentioned above. I will discuss that the resulting infinitely presented groups are acylindrically hyperbolic (joint work with A. Sisto). This generalization of the notion of Gromov hyperbolicity has strong analytic, algebraic, and geometric implications. The arguments rely on the Euler characteristic formula for planar 2-complexes and on a characterization of Gromov hyperbolic graphs through linear isoperimetric inequalities.
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